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Precalculus

Michael Sullivan

Chapter 6

Trigonometric Functions - all with Video Answers

Educators

Chapter Questions

01:26

Problem 1

Use transformations to graph y = 3x2.

Joseph Lentino
Joseph Lentino
Numerade Educator
00:16

Problem 1

The graph of $y=\frac{3 x-6}{x-4}$ has a vertical asymptote. What is it?

Victoria Karaluz
Victoria Karaluz
Numerade Educator
00:26

Problem 1

What is the formula for the circumference $C$ of a circle of radius $r$ ? What is the formula for the area $A$ of a circle of radius $r$ ?

Julie Silva
Julie Silva
Numerade Educator
00:08

Problem 1

In a right triangle, with legs $a$ and $b$ and hypotenuse $c$, the Pythagorean Theorem states that ____________

James Kiss
James Kiss
Numerade Educator
01:50

Problem 1

The domain of the function $f(x)=\frac{x+1}{2 x+1}$ is ____________.

Amit Srivastava
Amit Srivastava
Numerade Educator
00:46

Problem 1

For the graph of $y=A \sin (\omega x-\phi)$, the number $\frac{\phi}{\omega}$ is called the __________ _________.

Benjamin Schreyer
Benjamin Schreyer
Numerade Educator
02:45

Problem 2

Use transformations to graph y = 22x

Melissa Barry
Melissa Barry
Numerade Educator
02:19

Problem 2

True or False If $x=3$ is a vertical asymptote of the graph of a rational function $R$, then as $x \rightarrow 3,|R(x)| \rightarrow \infty$.

David Mccaslin
David Mccaslin
Numerade Educator
01:22

Problem 2

If an object has a speed of $r$ feet per second and travels a distance $d$ (in feet) in time $t$ (in seconds), then $d=$_______.

Abhijith V
Abhijith V
Numerade Educator
00:16

Problem 2

The value of the function $f(x)=3 x-7$ at 5 is ___.

James Kiss
James Kiss
Numerade Educator
00:27

Problem 2

A function for which $f(x)=f(-x)$ for all $x$ in the domain of $f$ is called a(n) _______ function.

Stephanie Gaston
Stephanie Gaston
Numerade Educator
00:36

Problem 2

True or False A graphing utility requires only two data points to find the sine function of best fit.

Joseph Lentino
Joseph Lentino
Numerade Educator
01:55

Problem 3

The maximum value of $y=\sin x, 0 \leq x \leq 2 \pi$, is_________ and occurs at $x=$_________

Micah Hurewitz
Micah Hurewitz
Numerade Educator
03:57

Problem 3

The graph of $y=\tan x$ is symmetric with respect to the___________ and has vertical asymptotes at___________

Darin Brion
Darin Brion
Numerade Educator
00:32

Problem 3

An angle $\theta$ is in __________ __________ if its vertex is at the origin of a rectangular coordinate system and its initial side coincides with the positive $x$-axis.

Katelyn Chen
Katelyn Chen
Numerade Educator
00:17

Problem 3

True or False For a function $y=f(x)$, for each $x$ in the domain, there is exactly one element $y$ in the range.

James Kiss
James Kiss
Numerade Educator
01:18

Problem 3

True or False The function $f(x)=\sqrt{x}$ is even.

Amit Srivastava
Amit Srivastava
Numerade Educator
06:20

Problem 3

Find the amplitude (if one exists), period, and phase shift of each function. Graph each function. Be sure to label key points Show at least two periods.

$y=4 \sin (2 x-\pi)$

Ziya Ogron
Ziya Ogron
Numerade Educator
03:26

Problem 4

If the function $y=A \sin (\omega x), A>0$, has amplitude 3 and period 2, then $A=$ _________and $\omega=$_________

Micah Hurewitz
Micah Hurewitz
Numerade Educator
03:03

Problem 4

The graph of $y=\sec x$ is symmetric with respect to the___________ and has vertical asymptotes at___________

Suman Saurav Thakur
Suman Saurav Thakur
Numerade Educator
00:30

Problem 4

A ________ ________ is a positive angle whose vertex is at the center of a circle.

Katelyn Chen
Katelyn Chen
Numerade Educator
00:14

Problem 4

If two triangles are similar, then corresponding angles are _______ and the lengths of corresponding sides are _______________.

James Kiss
James Kiss
Numerade Educator
01:57

Problem 4

True or False The equation $x^2+2 x=(x+1)^2-1$ is an identity.

Amit Srivastava
Amit Srivastava
Numerade Educator
06:29

Problem 4

Find the amplitude (if one exists), period, and phase shift of each function. Graph each function. Be sure to label key points Show at least two periods.

$y=3 \sin (3 x-\pi)$

Ziya Ogron
Ziya Ogron
Numerade Educator
02:22

Problem 5

The function $y=-3 \cos (6 x)$ has amplitude_________ and period_________

Micah Hurewitz
Micah Hurewitz
Numerade Educator
01:18

Problem 5

It is easiest to graph $y=\sec x$ by first sketching the graph of___________
(a) $y=\sin x$
(b) $y=\cos x$
(c) $y=\tan x$
(d) $y=\csc x$

Raushan Kumar
Raushan Kumar
Numerade Educator
01:24

Problem 5

Multiple Choice If the radius of a circle is $r$ and the length of the arc subtended by a central angle is also $r$, then the measure of the angle is 1 ______.
(a) degree
(b) minute
(c) second
(d) radian

Abhijith V
Abhijith V
Numerade Educator
00:31

Problem 5

What point is symmetric with respect to the $y$-axis to the point $\left(\frac{1}{2}, \frac{\sqrt{3}}{2}\right)$ ? (pp. 49-51)

James Kiss
James Kiss
Numerade Educator
00:37

Problem 5

The sine, cosine, cosecant, and secant functions have period ____; the tangent and cotangent functions have period ___.

Stephanie Gaston
Stephanie Gaston
Numerade Educator
05:36

Problem 5

Find the amplitude (if one exists), period, and phase shift of each function. Graph each function. Be sure to label key points Show at least two periods.

$y=3 \cos (2 x+\pi)$

Ziya Ogron
Ziya Ogron
Numerade Educator
01:35

Problem 6

True or False The graphs of $y=\sin x$ and $y=\cos x$ are identical except for a horizontal shift.

Micah Hurewitz
Micah Hurewitz
Numerade Educator
02:42

Problem 6

True or False The graphs of $y=\tan x, y=\cot x, y=\sec x$, and $y=\csc x$ each have infinitely many vertical asymptotes.

Victoria Karaluz
Victoria Karaluz
Numerade Educator
01:01

Problem 6

Problems are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

Find the domain of $f(x)=\sqrt[4]{5 x-2}-3$.

Yujie Wang
Yujie Wang
College of San Mateo
00:23

Problem 6

On a circle of radius $r$, a central angle of $\theta$ radians subtends an arc of length $s=$ _____; the area of the sector formed by this angle $\theta$ is $A=$______.

Katelyn Chen
Katelyn Chen
Numerade Educator
01:03

Problem 6

If $(x, y)$ is a point on the unit circle in quadrant IV and if $x=\frac{\sqrt{3}}{2}$, what is $y$ ? (p. 72)

James Kiss
James Kiss
Numerade Educator
00:59

Problem 6

The domain of the tangent function is ___________.

Amit Srivastava
Amit Srivastava
Numerade Educator
06:05

Problem 6

Find the amplitude (if one exists), period, and phase shift of each function. Graph each function. Be sure to label key points Show at least two periods.

$y=2 \cos \left(3 x+\frac{\pi}{2}\right)$

Ziya Ogron
Ziya Ogron
Numerade Educator
02:49

Problem 7

True or False For $y=2 \sin (\pi x)$, the amplitude is 2 and the period is $\frac{\pi}{2}$.

Micah Hurewitz
Micah Hurewitz
Numerade Educator
01:38

Problem 7

If necessary, refer to the graphs of the functions to answer each question.

What is the $y$-intercept of $y=\tan x$ ?

David Mccaslin
David Mccaslin
Numerade Educator
00:22

Problem 7

$180^{\circ}=$ radians
(a) $\frac{\pi}{2}$
(b) $\pi$
(c) $\frac{3 \pi}{2}$
(d) $2 \pi$

Katelyn Chen
Katelyn Chen
Numerade Educator
00:25

Problem 7

Which function takes as input a real number $t$ that corresponds to a point $P=(x, y)$ on the unit circle and outputs the $x$-coordinate?
(a) sine
(b) cosine
(c) tangent
(d) secant

James Kiss
James Kiss
Numerade Educator
01:25

Problem 7

Multiple Choice Which of the following is not in the range of the sine function?
(a) $\frac{\pi}{4}$
(b) $\frac{3}{2}$
(c) -0.37
(d) -1

Abdul Vahid M
Abdul Vahid M
Numerade Educator
05:10

Problem 7

Find the amplitude (if one exists), period, and phase shift of each function. Graph each function. Be sure to label key points Show at least two periods.

$y=-2 \cos \left(2 x-\frac{\pi}{2}\right)$

Ziya Ogron
Ziya Ogron
Numerade Educator
01:11

Problem 8

True or False The graph of the sine function has infinitely many $x$-intercepts.

Micah Hurewitz
Micah Hurewitz
Numerade Educator
02:04

Problem 8

If necessary, refer to the graphs of the functions to answer each question.

What is the $y$-intercept of $y=\cot x$ ?

David Mccaslin
David Mccaslin
Numerade Educator
00:17

Problem 8

An object travels on a circle of radius $r$ with constant speed. If $s$ is the distance traveled in time $t$ on the circle and $\theta$ is the central angle (in radians) swept out in time $t$, then the linear speed of the object is $v=$ and the angular speed of the object is $\omega=$

Katelyn Chen
Katelyn Chen
Numerade Educator
00:33

Problem 8

The point on the unit circle that corresponds to $\theta=\frac{\pi}{2}$ is $P=$

James Kiss
James Kiss
Numerade Educator
02:37

Problem 8

Which of the following functions is even?
(a) cosine
(b) sine
(c) tangent
(d) cosecant

Stephanie Gaston
Stephanie Gaston
Numerade Educator
05:42

Problem 8

Find the amplitude (if one exists), period, and phase shift of each function. Graph each function. Be sure to label key points Show at least two periods.

$y=-3 \sin \left(2 x+\frac{\pi}{2}\right)$

Ziya Ogron
Ziya Ogron
Numerade Educator
02:18

Problem 9

One period of the graph of $y=\sin (\omega x)$ or $y=\cos (\omega x)$ is called $a(n)$
(a) amplitude
(b) phase shift
(c) transformation
(d) cycle

Micah Hurewitz
Micah Hurewitz
Numerade Educator
02:25

Problem 9

If necessary, refer to the graphs of the functions to answer each question.

What is the $y$-intercept of $y=\csc x$ ?

David Mccaslin
David Mccaslin
Numerade Educator
00:39

Problem 9

True or False The angular speed $\omega$ of an object traveling on a circle of radius $r$ is the angle $\theta$ (measured in radians) swept out, divided by the elapsed time $t$.

Katelyn Chen
Katelyn Chen
Numerade Educator
00:24

Problem 9

The point on the unit circle that corresponds to $\theta=\frac{\pi}{4}$ is
$$
P=
$$

James Kiss
James Kiss
Numerade Educator
02:19

Problem 9

$\sin ^2 \theta+\cos ^2 \theta=$

Amit Srivastava
Amit Srivastava
Numerade Educator
06:40

Problem 9

Find the amplitude (if one exists), period, and phase shift of each function. Graph each function. Be sure to label key points Show at least two periods.

$y=2 \cos (2 \pi x+4)+4$

Ziya Ogron
Ziya Ogron
Numerade Educator
04:19

Problem 10

To graph $y=3 \sin (-2 x)$ using key points, the equivalent form could be graphed instead.
(a) $y=-3 \sin (-2 x)$
(b) $y=-2 \sin (3 x)$
(c) $y=3 \sin (2 x)$
(d) $y=-3 \sin (2 x)$

Micah Hurewitz
Micah Hurewitz
Numerade Educator
01:40

Problem 10

If necessary, refer to the graphs of the functions to answer each question.

What is the $y$-intercept of $y=\sec x$ ?

David Mccaslin
David Mccaslin
Numerade Educator
01:03

Problem 10

True or False For circular motion on a circle of radius $r$, linear speed equals angular speed divided by $r$.

Katelyn Chen
Katelyn Chen
Numerade Educator
01:15

Problem 10

True or False Exact values can be found for the sine of any angle.

Ethan Somes
Ethan Somes
Numerade Educator
00:29

Problem 10

True or False $\sec \theta=\frac{1}{\sin \theta}$

Amit Srivastava
Amit Srivastava
Numerade Educator
06:49

Problem 10

Find the amplitude (if one exists), period, and phase shift of each function. Graph each function. Be sure to label key points Show at least two periods.

$y=4 \sin (\pi x+2)-5$

Ziya Ogron
Ziya Ogron
Numerade Educator
09:29

Problem 11

$$
f(x)=\sin x
$$
(a) What is the $y$-intercept of the graph of $f$ ?
(b) For what numbers $x,-\pi \leq x \leq \pi$, is the graph of $f$ increasing?
(c) What is the absolute maximum of $f$ ?
(d) For what numbers $x, 0 \leq x \leq 2 \pi$, does $f(x)=0$ ?
(e) For what numbers $x,-2 \pi \leq x \leq 2 \pi$, does $f(x)=1$ ? Where does $f(x)=-1$ ?
(f) For what numbers $x,-2 \pi \leq x \leq 2 \pi$, does $f(x)=-\frac{1}{2}$ ?
(g) What are the $x$-intercepts of $f$ ?

Micah Hurewitz
Micah Hurewitz
Numerade Educator
03:19

Problem 11

If necessary, refer to the graphs of the functions to answer each question.

For what numbers $x,-2 \pi \leq x \leq 2 \pi$, does $\csc x=1$ ? For what numbers $x$ does $\csc x=-1$ ?

David Mccaslin
David Mccaslin
Numerade Educator
01:11

Problem 11

Draw each angle in standard position.

$30^{\circ}$

Abhijith V
Abhijith V
Numerade Educator
00:23

Problem 11

For any angle $\theta$ in standard position, let $P=(x, y)$ be the point on the terminal side of $\theta$ that is also on the circle $x^2+y^2=r^2$. Then, $\sin \theta=\ldots$ and $\cos \theta=$

James Kiss
James Kiss
Numerade Educator
00:39

Problem 11

Use the fact that the trigonometric functions are periodic to find the exact value of each expression. Do not use a calculator.

$\sin 405^{\circ}$

Amit Srivastava
Amit Srivastava
Numerade Educator
06:19

Problem 11

Find the amplitude (if one exists), period, and phase shift of each function. Graph each function. Be sure to label key points Show at least two periods.

$y=2 \cos (2 \pi x-4)-1$

Ziya Ogron
Ziya Ogron
Numerade Educator
10:23

Problem 12

$$
g(x)=\cos x
$$
(a) What is the $y$-intercept of the graph of $g$ ?
(b) For what numbers $x,-\pi \leq x \leq \pi$, is the graph of $g$ decreasing?
(c) What is the absolute minimum of $g$ ?
(d) For what numbers $x, 0 \leq x \leq 2 \pi$, does $g(x)=0$ ?
(e) For what numbers $x,-2 \pi \leq x \leq 2 \pi$, does $g(x)=1$ ? Where does $g(x)=-1$ ?
(f) For what numbers $x,-2 \pi \leq x \leq 2 \pi$, does $g(x)=\frac{\sqrt{3}}{2}$ ?
(g) What are the $x$-intercepts of $g$ ?

Micah Hurewitz
Micah Hurewitz
Numerade Educator
03:30

Problem 12

If necessary, refer to the graphs of the functions to answer each question.

For what numbers $x,-2 \pi \leq x \leq 2 \pi$, does $\sec x=1$ ? For what numbers $x$ does $\sec x=-1$ ?

David Mccaslin
David Mccaslin
Numerade Educator
01:08

Problem 12

Draw each angle in standard position.

$60^{\circ}$

Abhijith V
Abhijith V
Numerade Educator
01:14

Problem 12

The point on the unit circle that corresponds to $\theta=\frac{\pi}{3}$ is
(a) $\left(\frac{1}{2}, \frac{\sqrt{3}}{2}\right)$
(b) $\left(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)$
(c) $\left(\frac{\sqrt{3}}{2}, \frac{1}{2}\right)$
(d) $\left(\sqrt{3}, \frac{2 \sqrt{3}}{3}\right)$

Abhijith V
Abhijith V
Numerade Educator
00:44

Problem 12

Use the fact that the trigonometric functions are periodic to find the exact value of each expression. Do not use a calculator.

$\cos 420^{\circ}$

Amit Srivastava
Amit Srivastava
Numerade Educator
05:25

Problem 12

Find the amplitude (if one exists), period, and phase shift of each function. Graph each function. Be sure to label key points Show at least two periods.

$y=3 \cos (\pi x-2)+5$

Ziya Ogron
Ziya Ogron
Numerade Educator
00:48

Problem 13

Determine the amplitude and period of each function without graphing.

$y=3 \cos x$

Micah Hurewitz
Micah Hurewitz
Numerade Educator
02:25

Problem 13

If necessary, refer to the graphs of the functions to answer each question.

For what numbers $x,-2 \pi \leq x \leq 2 \pi$, does the graph of $y=\csc x$ have vertical asymptotes?

David Mccaslin
David Mccaslin
Numerade Educator
01:36

Problem 13

Draw each angle in standard position.

$-120^{\circ}$

Abhijith V
Abhijith V
Numerade Educator
02:24

Problem 13

P $=(x, y)$ is the point on the unit circle that corresponds to a real number . Find the exact values of the six trigonometric functions of $t$.

$\left(\frac{\sqrt{3}}{2}, \frac{1}{2}\right)$

James Kiss
James Kiss
Numerade Educator
00:39

Problem 13

Use the fact that the trigonometric functions are periodic to find the exact value of each expression. Do not use a calculator.

$\sin 390^{\circ}$

Amit Srivastava
Amit Srivastava
Numerade Educator
05:01

Problem 13

Find the amplitude (if one exists), period, and phase shift of each function. Graph each function. Be sure to label key points Show at least two periods.

$y=-3 \cos \left(-2 x+\frac{\pi}{2}\right)$

Ziya Ogron
Ziya Ogron
Numerade Educator
00:48

Problem 14

Determine the amplitude and period of each function without graphing.

$y=5 \sin x$

Raushan Kumar
Raushan Kumar
Numerade Educator
02:44

Problem 14

If necessary, refer to the graphs of the functions to answer each question.

For what numbers $x,-2 \pi \leq x \leq 2 \pi$, does the graph of $y=\sec x$ have vertical asymptotes?

David Mccaslin
David Mccaslin
Numerade Educator
01:13

Problem 14

Draw each angle in standard position.

$135^{\circ}$

Abhijith V
Abhijith V
Numerade Educator
02:21

Problem 14

P $=(x, y)$ is the point on the unit circle that corresponds to a real number . Find the exact values of the six trigonometric functions of $t$.

$\left(\frac{1}{2},-\frac{\sqrt{3}}{2}\right)$

James Kiss
James Kiss
Numerade Educator
00:31

Problem 14

Use the fact that the trigonometric functions are periodic to find the exact value of each expression. Do not use a calculator.

$\tan 405^{\circ}$

Amit Srivastava
Amit Srivastava
Numerade Educator
05:42

Problem 14

Find the amplitude (if one exists), period, and phase shift of each function. Graph each function. Be sure to label key points Show at least two periods.

$y=-3 \sin \left(-2 x+\frac{\pi}{2}\right)$

Ziya Ogron
Ziya Ogron
Numerade Educator
01:15

Problem 15

Determine the amplitude and period of each function without graphing.

$y=-\sin \left(\frac{1}{2} x\right)$

Micah Hurewitz
Micah Hurewitz
Numerade Educator
03:13

Problem 15

If necessary, refer to the graphs of the functions to answer each question.

For what numbers $x,-2 \pi \leq x \leq 2 \pi$, does the graph of $y=\tan x$ have vertical asymptotes?

David Mccaslin
David Mccaslin
Numerade Educator
01:11

Problem 15

Draw each angle in standard position.

$540^{\circ}$

Abhijith V
Abhijith V
Numerade Educator
03:11

Problem 15

P $=(x, y)$ is the point on the unit circle that corresponds to a real number . Find the exact values of the six trigonometric functions of $t$.

$\left(-\frac{1}{5}, \frac{2 \sqrt{6}}{5}\right)$

James Kiss
James Kiss
Numerade Educator
00:38

Problem 15

Use the fact that the trigonometric functions are periodic to find the exact value of each expression. Do not use a calculator.

$\sec 540^{\circ}$

Amit Srivastava
Amit Srivastava
Numerade Educator
06:01

Problem 15

Find the amplitude (if one exists), period, and phase shift of each function. Graph each function. Be sure to label key points Show at least two periods.

$y=\frac{1}{2} \cot (2 x-\pi)$

Ziya Ogron
Ziya Ogron
Numerade Educator
01:03

Problem 16

Determine the amplitude and period of each function without graphing.

$y=-3 \cos (4 x)$

Raushan Kumar
Raushan Kumar
Numerade Educator
02:49

Problem 16

If necessary, refer to the graphs of the functions to answer each question.

For what numbers $x,-2 \pi \leq x \leq 2 \pi$, does the graph of $y=\cot x$ have vertical asymptotes?

David Mccaslin
David Mccaslin
Numerade Educator
01:12

Problem 16

Draw each angle in standard position.

$450^{\circ}$

Abhijith V
Abhijith V
Numerade Educator
02:09

Problem 16

P $=(x, y)$ is the point on the unit circle that corresponds to a real number . Find the exact values of the six trigonometric functions of $t$.

$\left(-\frac{2}{5}, \frac{\sqrt{21}}{5}\right)$

James Kiss
James Kiss
Numerade Educator
00:45

Problem 16

Use the fact that the trigonometric functions are periodic to find the exact value of each expression. Do not use a calculator.

$\csc 450^{\circ}$

Amit Srivastava
Amit Srivastava
Numerade Educator
06:12

Problem 16

Find the amplitude (if one exists), period, and phase shift of each function. Graph each function. Be sure to label key points Show at least two periods.

$y=2 \tan (4 x-\pi)$

Ziya Ogron
Ziya Ogron
Numerade Educator
01:15

Problem 17

Determine the amplitude and period of each function without graphing.

$y=6 \sin (\pi x)$

Micah Hurewitz
Micah Hurewitz
Numerade Educator
04:01

Problem 17

Graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function.

$y=-2 \tan x$

David Mccaslin
David Mccaslin
Numerade Educator
01:16

Problem 17

Draw each angle in standard position.

$\frac{4 \pi}{3}$

Abhijith V
Abhijith V
Numerade Educator
01:19

Problem 17

P $=(x, y)$ is the point on the unit circle that corresponds to a real number . Find the exact values of the six trigonometric functions of $t$.

$\left(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)$

James Kiss
James Kiss
Numerade Educator
00:41

Problem 17

Use the fact that the trigonometric functions are periodic to find the exact value of each expression. Do not use a calculator.

$\sec 420^{\circ}$

Amit Srivastava
Amit Srivastava
Numerade Educator
06:03

Problem 17

Find the amplitude (if one exists), period, and phase shift of each function. Graph each function. Be sure to label key points Show at least two periods.

$y=\frac{1}{2} \sec (3 x-\pi)$

Ziya Ogron
Ziya Ogron
Numerade Educator
01:19

Problem 18

Determine the amplitude and period of each function without graphing.

$y=-3 \cos (3 x)$

Micah Hurewitz
Micah Hurewitz
Numerade Educator
04:17

Problem 18

Graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function.

$y=3 \tan x$

David Mccaslin
David Mccaslin
Numerade Educator
01:22

Problem 18

Draw each angle in standard position.

$\frac{3 \pi}{4}$

Abhijith V
Abhijith V
Numerade Educator
01:50

Problem 18

P $=(x, y)$ is the point on the unit circle that corresponds to a real number . Find the exact values of the six trigonometric functions of $t$.

$\left(-\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)$

James Kiss
James Kiss
Numerade Educator
00:51

Problem 18

Use the fact that the trigonometric functions are periodic to find the exact value of each expression. Do not use a calculator.

$\cot 390^{\circ}$

Amit Srivastava
Amit Srivastava
Numerade Educator
06:40

Problem 18

Find the amplitude (if one exists), period, and phase shift of each function. Graph each function. Be sure to label key points Show at least two periods.

$y=3 \csc \left(2 x-\frac{\pi}{4}\right)$

Ziya Ogron
Ziya Ogron
Numerade Educator
01:15

Problem 19

Determine the amplitude and period of each function without graphing.

$y=\frac{4}{3} \sin \left(\frac{2}{3} x\right)$

Micah Hurewitz
Micah Hurewitz
Numerade Educator
03:41

Problem 19

Graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function.

$y=-3 \cot x$

David Mccaslin
David Mccaslin
Numerade Educator
01:44

Problem 19

Draw each angle in standard position.

$-\frac{2 \pi}{3}$

Abhijith V
Abhijith V
Numerade Educator
01:46

Problem 19

P $=(x, y)$ is the point on the unit circle that corresponds to a real number . Find the exact values of the six trigonometric functions of $t$.

$\left(-\frac{\sqrt{5}}{3},-\frac{2}{3}\right)$

James Kiss
James Kiss
Numerade Educator
00:45

Problem 19

Use the fact that the trigonometric functions are periodic to find the exact value of each expression. Do not use a calculator.

$\sin \frac{9 \pi}{4}$

Amit Srivastava
Amit Srivastava
Numerade Educator
01:36

Problem 19

Write an equation of a sine function that has the given characteristics.

Amplitude: 3
Period: $\frac{\pi}{2}$
Phase shift: 2

Joseph Lentino
Joseph Lentino
Numerade Educator
00:58

Problem 20

Determine the amplitude and period of each function without graphing.

$y=-\frac{1}{7} \cos \left(\frac{7}{2} x\right)$

Raushan Kumar
Raushan Kumar
Numerade Educator
01:52

Problem 20

Graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function.

$y=4 \cot x$

Sheryl Ezze
Sheryl Ezze
Numerade Educator
01:51

Problem 20

Draw each angle in standard position.

$-\frac{\pi}{6}$

Abhijith V
Abhijith V
Numerade Educator
01:47

Problem 20

P $=(x, y)$ is the point on the unit circle that corresponds to a real number . Find the exact values of the six trigonometric functions of $t$.

$\left(\frac{2 \sqrt{2}}{3},-\frac{1}{3}\right)$

James Kiss
James Kiss
Numerade Educator
00:48

Problem 20

Use the fact that the trigonometric functions are periodic to find the exact value of each expression. Do not use a calculator.

$\cos \frac{33 \pi}{4}$

Amit Srivastava
Amit Srivastava
Numerade Educator
01:16

Problem 20

Write an equation of a sine function that has the given characteristics.

Amplitude: 2
Period: $\pi$
Phase shift: $\frac{1}{2}$

Joseph Lentino
Joseph Lentino
Numerade Educator
01:09

Problem 21

Determine the amplitude and period of each function without graphing.

$y=\frac{9}{5} \cos \left(-\frac{3 \pi}{2} x\right)$

Micah Hurewitz
Micah Hurewitz
Numerade Educator
02:02

Problem 21

Graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function.

$y=\tan \left(\frac{\pi}{2} x\right)$

Sheryl Ezze
Sheryl Ezze
Numerade Educator
01:49

Problem 21

Draw each angle in standard position.

$\frac{21 \pi}{4}$

Abhijith V
Abhijith V
Numerade Educator
00:58

Problem 21

Find the exact value. Do not use a calculator.

$\sin \frac{11 \pi}{2}$

James Kiss
James Kiss
Numerade Educator
00:42

Problem 21

Use the fact that the trigonometric functions are periodic to find the exact value of each expression. Do not use a calculator.

$\csc \frac{9 \pi}{2}$

Amit Srivastava
Amit Srivastava
Numerade Educator
01:40

Problem 21

Write an equation of a sine function that has the given characteristics.

Amplitude: 2
Period: $\pi$
Phase shift: -2

Joseph Lentino
Joseph Lentino
Numerade Educator
01:00

Problem 22

Determine the amplitude and period of each function without graphing.

$y=\frac{10}{9} \sin \left(-\frac{2 \pi}{5} x\right)$

Raushan Kumar
Raushan Kumar
Numerade Educator
02:04

Problem 22

Graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function.

$y=\tan \left(\frac{1}{2} x\right)$

Sheryl Ezze
Sheryl Ezze
Numerade Educator
02:03

Problem 22

Draw each angle in standard position.

$\frac{16 \pi}{3}$

Abhijith V
Abhijith V
Numerade Educator
00:42

Problem 22

Find the exact value. Do not use a calculator.

$\cos (7 \pi)$

James Kiss
James Kiss
Numerade Educator
00:41

Problem 22

Use the fact that the trigonometric functions are periodic to find the exact value of each expression. Do not use a calculator.

$\tan (21 \pi)$

Amit Srivastava
Amit Srivastava
Numerade Educator
01:23

Problem 22

Write an equation of a sine function that has the given characteristics.

Amplitude: 3
Period: $3 \pi$
Phase shift: $-\frac{1}{3}$

Joseph Lentino
Joseph Lentino
Numerade Educator
01:17

Problem 23

Match the given function to one of the graphs (A)–(J).

$y=2 \cos \left(\frac{\pi}{2} x\right)$

Micah Hurewitz
Micah Hurewitz
Numerade Educator
04:10

Problem 23

Graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function.

$y=\cot \left(\frac{1}{4} x\right)$

David Mccaslin
David Mccaslin
Numerade Educator
00:54

Problem 23

Convert each angle in degrees to radians. Express your answer as a multiple of $\pi$.

$30^{\circ}$

Suman Saurav Thakur
Suman Saurav Thakur
Numerade Educator
00:55

Problem 23

Find the exact value. Do not use a calculator.

$\cot \frac{7 \pi}{2}$

James Kiss
James Kiss
Numerade Educator
00:56

Problem 23

Use the fact that the trigonometric functions are periodic to find the exact value of each expression. Do not use a calculator.

$\cot \frac{17 \pi}{4}$

Amit Srivastava
Amit Srivastava
Numerade Educator
06:11

Problem 23

The current $I$, in amperes, flowing through an ac (alternating current) circuit at time $t$, in seconds, is
$$
I(t)=220 \sin \left(60 \pi t-\frac{\pi}{6}\right) \quad t \geq 0
$$

Sheryl Ezze
Sheryl Ezze
Numerade Educator
01:46

Problem 24

Match the given function to one of the graphs (A)–(J).

$y=2 \sin \left(\frac{\pi}{2} x\right)$

Micah Hurewitz
Micah Hurewitz
Numerade Educator
03:23

Problem 24

Graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function.

$y=\cot \left(\frac{\pi}{4} x\right)$

David Mccaslin
David Mccaslin
Numerade Educator
00:42

Problem 24

Convert each angle in degrees to radians. Express your answer as a multiple of $\pi$.

$120^{\circ}$

Julie Silva
Julie Silva
Numerade Educator
00:52

Problem 24

Find the exact value. Do not use a calculator.

$\tan (6 \pi)$

James Kiss
James Kiss
Numerade Educator
00:55

Problem 24

Use the fact that the trigonometric functions are periodic to find the exact value of each expression. Do not use a calculator.

$\sec \frac{17 \pi}{4}$

Amit Srivastava
Amit Srivastava
Numerade Educator
04:57

Problem 24

The current $I$, in amperes, flowing through an ac (alternating current) circuit at time $t$, in seconds, is
$$
I(t)=120 \sin \left(30 \pi t-\frac{\pi}{3}\right) \quad t \geq 0
$$
What is the period? What is the amplitude? What is the phase shift? Graph this function over two periods.

Ziya Ogron
Ziya Ogron
Numerade Educator
01:21

Problem 25

Match the given function to one of the graphs (A)–(J).

$y=3 \cos (2 x)$

Micah Hurewitz
Micah Hurewitz
Numerade Educator
03:10

Problem 25

Graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function.

$y=\frac{1}{2} \csc x$

David Mccaslin
David Mccaslin
Numerade Educator
00:42

Problem 25

Convert each angle in degrees to radians. Express your answer as a multiple of $\pi$.

$330^{\circ}$

Julie Silva
Julie Silva
Numerade Educator
00:40

Problem 25

Find the exact value. Do not use a calculator.

$\sec (8 \pi)$

James Kiss
James Kiss
Numerade Educator
01:02

Problem 25

Use the fact that the trigonometric functions are periodic to find the exact value of each expression. Do not use a calculator.

$\sec \frac{25 \pi}{6}$

Amit Srivastava
Amit Srivastava
Numerade Educator
11:14

Problem 25

Hurricanes are categorized using the Saffir-Simpson Hurricane Scale, with winds $111-130$ miles per hour ( $\mathrm{mph}$ ) corresponding to a category 3 hurricane, winds 131-155 mph corresponding to a category 4 hurricane, and winds in excess of $155 \mathrm{mph}$ corresponding to a category 5 hurricane. The data on the right represent the number of major hurricanes in the Atlantic Basin (category 3,4 , or 5 ) each decade from 1921 to 2010.
(a) Draw a scatter plot of the data.
(b) Find a sinusoidal function of the form $y=A \sin (\omega x-\phi)+B$ that models the data.
(c) Draw the sinusoidal function found in part (b) on the scatter plot.
(d) Use a graphing utility to find the sinusoidal function of best fit.
(e) Graph the sinusoidal function of best fit on a scatter plot of the data.

Ziya Ogron
Ziya Ogron
Numerade Educator
01:52

Problem 26

Match the given function to one of the graphs (A)–(J).

$y=2 \cos \left(\frac{1}{2} x\right)$

AN
Austin Norman
Numerade Educator
01:30

Problem 26

Graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function.

$y=2 \sec x$

Victoria Karaluz
Victoria Karaluz
Numerade Educator
01:24

Problem 26

Convert each angle in degrees to radians. Express your answer as a multiple of $\pi$.

$495^{\circ}$

Abhijith V
Abhijith V
Numerade Educator
00:51

Problem 26

Find the exact value. Do not use a calculator.

$\csc \frac{11 \pi}{2}$

James Kiss
James Kiss
Numerade Educator
01:02

Problem 26

Use the fact that the trigonometric functions are periodic to find the exact value of each expression. Do not use a calculator.

$\tan \frac{19 \pi}{6}$

Amit Srivastava
Amit Srivastava
Numerade Educator
09:50

Problem 26

The data on the next page represent the average monthly temperatures for Washington, D.C.
(a) Draw a scatter plot of the data for one period.
(b) Find a sinusoidal function of the form $y=A \sin (\omega x-\phi)+B$ that models the data.
$$
\begin{array}{|lc|}
\hline \text { Decade, } \boldsymbol{x} & \text { Major Hurricanes, } \boldsymbol{H} \\
\hline 1921-1930,1 & 17 \\
1931-1940,2 & 16 \\
1941-1950,3 & 29 \\
1951-1960,4 & 33 \\
1961-1970,5 & 27 \\
1971-1980,6 & 16 \\
1981-1990,7 & 16 \\
1991-2000,8 & 27 \\
2001-2010,9 & 33 \\
\hline
\end{array}
$$
(c) Draw the sinusoidal function found in part (b) on the scatter plot.
(d) Use a graphing utility to find the sinusoidal function of best fit.
(e) Graph the sinusoidal function of best fit on a scatter plot of the data.
$$
\begin{array}{|ll|}
\hline \text { Month, } \boldsymbol{x} & \begin{array}{c}
\text { Average Monthly } \\
\text { Temperature, }
\end{array}{ }^{\circ} \mathrm{F} \\
\hline \text { January, 1 } & 36.0 \\
\text { February, 2 } & 39.0 \\
\text { March, 3 } & 46.8 \\
\text { April, } 4 & 56.8 \\
\text { May, } 5 & 66.0 \\
\text { June, 6 } & 75.2 \\
\text { July, 7 } & 79.8 \\
\text { August, 8 } & 78.1 \\
\text { September, 9 } & 71.0 \\
\text { October, 10 } & 59.5 \\
\text { November, 11 } & 49.6 \\
\text { December, 12 } & 39.7 \\
\hline
\end{array}
$$

Ziya Ogron
Ziya Ogron
Numerade Educator
01:58

Problem 27

Match the given function to one of the graphs (A)–(J).

$y=2 \sin \left(\frac{1}{2} x\right)$

AN
Austin Norman
Numerade Educator
03:25

Problem 27

Graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function.

$y=-4 \sec x$

David Mccaslin
David Mccaslin
Numerade Educator
00:30

Problem 27

Convert each angle in degrees to radians. Express your answer as a multiple of $\pi$.

$-30^{\circ}$

Julie Silva
Julie Silva
Numerade Educator
00:51

Problem 27

Find the exact value. Do not use a calculator.

$\sin (-3 \pi)$

James Kiss
James Kiss
Numerade Educator
01:46

Problem 27

Name the quadrant in which the angle $\theta$ lies.

$\sin \theta>0, \quad \cos \theta<0$

Urjeet Deshmukh
Urjeet Deshmukh
Numerade Educator
09:03

Problem 27

The following data represent the average monthly temperatures for Baltimore, Maryland.
(a) Draw a scatter plot of the data for one period.
(b) Find a sinusoidal function of the form $y=A \sin (\omega x-\phi)+B$ that models the data.
(c) Draw the sinusoidal function found in part (b) on the scatter plot.
(d) Use a graphing utility to find the sinusoidal function of best fit.
(e) Graph the sinusoidal function of best fit on a scatter plot of the data.
$$
\begin{array}{|lc|}
\hline \text { Month, } \boldsymbol{x} & \begin{array}{c}
\text { Average Monthly } \\
\text { Temperature, }^{\circ} \mathrm{F}
\end{array} \\
\hline \text { January, 1 } & 32.9 \\
\text { February, 2 } & 35.8 \\
\text { March, 3 } & 43.6 \\
\text { April, 4 } & 53.7 \\
\text { May, 5 } & 62.9 \\
\text { June, 6 } & 72.4 \\
\text { July, 7 } & 77.0 \\
\text { August, 8 } & 75.1 \\
\text { September, 9 } & 67.8 \\
\text { October, 10 } & 56.1 \\
\text { November, 11 } & 46.5 \\
\text { December, 12 } & 36.7 \\
\hline
\end{array}
$$

Ziya Ogron
Ziya Ogron
Numerade Educator
01:18

Problem 28

Match the given function to one of the graphs (A)–(J).

$y=-3 \sin (2 x)$

Micah Hurewitz
Micah Hurewitz
Numerade Educator
01:46

Problem 28

Graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function.

$y=-3 \csc x$

Victoria Karaluz
Victoria Karaluz
Numerade Educator
00:38

Problem 28

Convert each angle in degrees to radians. Express your answer as a multiple of $\pi$.

$-60^{\circ}$

Julie Silva
Julie Silva
Numerade Educator
00:44

Problem 28

Find the exact value. Do not use a calculator.

$\cos \left(-\frac{3 \pi}{2}\right)$

James Kiss
James Kiss
Numerade Educator
01:24

Problem 28

Name the quadrant in which the angle $\theta$ lies.

$\sin \theta<0, \quad \cos \theta>0$

Urjeet Deshmukh
Urjeet Deshmukh
Numerade Educator
09:33

Problem 28

The following data represent the average monthly temperatures for Indianapolis, Indiana.
(a) Draw a scatter plot of the data for one period.
(b) Find a sinusoidal function of the form
$$
y=A \sin (\omega x-\phi)+B
$$
that models the data.
(c) Draw the sinusoidal function found in part (b) on the scatter plot.
(d) Use a graphing utility to find the sinusoidal function of best fit.
(e) Graph the sinusoidal function of best fit on a scatter plot of the data.
$$
\begin{array}{|lc|}
\hline \text { Month, } \boldsymbol{x} & \begin{array}{c}
\text { Average Monthly } \\
\text { Temperature, }{ }^{\circ} \mathrm{F}
\end{array} \\
\hline \text { January, 1 } & 28.1 \\
\text { February, 2 } & 32.1 \\
\text { March, 3 } & 42.2 \\
\text { April, 4 } & 53.0 \\
\text { May, 5 } & 62.7 \\
\text { June, 6 } & 72.0 \\
\text { July, 7 } & 75.4 \\
\text { August, 8 } & 74.2 \\
\text { September, 9 } & 66.9 \\
\text { October, 10 } & 55.0 \\
\text { November, 11 } & 43.6 \\
\text { December, 12 } & 31.6 \\
\hline
\end{array}
$$

Ziya Ogron
Ziya Ogron
Numerade Educator
01:17

Problem 29

Match the given function to one of the graphs (A)–(J).

$y=-2 \cos \left(\frac{\pi}{2} x\right)$

Micah Hurewitz
Micah Hurewitz
Numerade Educator
02:19

Problem 29

Graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function.

$y=4 \sec \left(\frac{1}{2} x\right)$

Sheryl Ezze
Sheryl Ezze
Numerade Educator
00:36

Problem 29

Convert each angle in degrees to radians. Express your answer as a multiple of $\pi$.

$270^{\circ}$

Julie Silva
Julie Silva
Numerade Educator
00:36

Problem 29

Find the exact value. Do not use a calculator.

$\tan (-3 \pi)$

James Kiss
James Kiss
Numerade Educator
01:51

Problem 29

Name the quadrant in which the angle $\theta$ lies.

$\cos \theta>0, \quad \tan \theta>0$

Urjeet Deshmukh
Urjeet Deshmukh
Numerade Educator
09:32

Problem 29

The length of time between consecutive high tides is 12 hours and 25 minutes. According to the National Oceanic and Atmospheric Administration, on Saturday, April 21,2018, in Sitka, Alaska, high tide occurred at 4:51 A? (4.85 hours) and low tide occurred at 11:50 AM (11.83 hours). Water heights are measured as the amounts above or below the mean lower low water. The height of the water at high tide was 10.03 feet, and the height of the water at low tide was -0.46 feet.
(a) Approximately when did the next high tide occur?
(b) Find a sinusoidal function of the form
$$
y=A \sin (\omega x-\phi)+B
$$
that models the data.
(c) Use the function found in part (b) to predict the height of the water at $3 \mathrm{pM}$.

Ziya Ogron
Ziya Ogron
Numerade Educator
01:39

Problem 30

Match the given function to one of the graphs (A)–(J).

$y=-2 \cos \left(\frac{1}{2} x\right)$

Micah Hurewitz
Micah Hurewitz
Numerade Educator
04:04

Problem 30

Graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function.

$y=\frac{1}{2} \csc (2 x)$

David Mccaslin
David Mccaslin
Numerade Educator
01:04

Problem 30

Convert each angle in degrees to radians. Express your answer as a multiple of $\pi$.

$540^{\circ}$

Abhijith V
Abhijith V
Numerade Educator
00:32

Problem 30

Find the exact value. Do not use a calculator.

$\sec (-\pi)$

James Kiss
James Kiss
Numerade Educator
02:06

Problem 30

Name the quadrant in which the angle $\theta$ lies.

$\sin \theta<0, \quad \tan \theta<0$

Urjeet Deshmukh
Urjeet Deshmukh
Numerade Educator
10:25

Problem 30

Suppose that the length of time between consecutive high tides is approximately 12.5 hours. According to the National Oceanic and Atmospheric Administration, on a particular day in a city in Georgia, high tide occurred at 3:36 AM (3.6000 hours) and low tide occurred at 10:06 AM (10.1000 hours). Water heights are measured as the amounts above or below the mean lower low water. The height of the water at high tide was 8.2 feet and the height of the water at low tide was -0.6 foot. Answer parts (a) through (c) below.
(a) Approximately when will the next high tide occur?
(b) Find a sinusoidal function of the form
$$
y=A \sin (\omega x-\phi)+B
$$
that fits the data.
(c) Use the function found in part (b) to predict the height of the water at the next high tide.

Sarvesh Somasundaram
Sarvesh Somasundaram
Numerade Educator
01:20

Problem 31

Match the given function to one of the graphs (A)–(J).

$y=-2 \sin \left(\frac{1}{2} x\right)$

Micah Hurewitz
Micah Hurewitz
Numerade Educator
02:29

Problem 31

Graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function.

$y=-3 \sec \left(\frac{\pi}{2} x\right)$

Sheryl Ezze
Sheryl Ezze
Numerade Educator
00:47

Problem 31

Convert each angle in degrees to radians. Express your answer as a multiple of $\pi$.

$-225^{\circ}$

Julie Silva
Julie Silva
Numerade Educator
00:25

Problem 31

Find the exact value of each expression. Do not use a calculator.

$\sin 30^{\circ}-\cos 45^{\circ}$

James Kiss
James Kiss
Numerade Educator
01:11

Problem 31

Name the quadrant in which the angle $\theta$ lies.

$\cos \theta<0, \quad \tan \theta>0$

Amit Srivastava
Amit Srivastava
Numerade Educator
13:44

Problem 31

According to the Old Farmer's Almanac, in Miami, Florida, the number of hours of sunlight on the summer solstice of 2018 was 13.75 , and the number of hours of sunlight on the winter solstice was 10.52.
(a) Find a sinusoidal function of the form
$$
y=A \sin (\omega x-\phi)+B
$$
that models the data.
(b) Use the function found in part (a) to predict the number of hours of sunlight on April 1, the 91st day of the year.
(c) Draw a graph of the function found in part (a).
(d) Look up the number of hours of sunlight for April 1 in the Old Farmer's Almanac, and compare the actual hours of daylight to the results found in part (b).

Ziya Ogron
Ziya Ogron
Numerade Educator
01:38

Problem 32

Match the given function to one of the graphs (A)–(J).

$y=3 \sin (2 x)$

Micah Hurewitz
Micah Hurewitz
Numerade Educator
02:06

Problem 32

Graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function.

$y=-2 \csc (\pi x)$

Sheryl Ezze
Sheryl Ezze
Numerade Educator
00:40

Problem 32

Convert each angle in degrees to radians. Express your answer as a multiple of $\pi$.

$-240^{\circ}$

Julie Silva
Julie Silva
Numerade Educator
00:36

Problem 32

Find the exact value of each expression. Do not use a calculator.

$\sin 45^{\circ}+\cos 60^{\circ}$

James Kiss
James Kiss
Numerade Educator
00:58

Problem 32

Name the quadrant in which the angle $\theta$ lies.

$\cos \theta>0, \quad \tan \theta<0$

Amit Srivastava
Amit Srivastava
Numerade Educator
12:00

Problem 32

According to the Old Farmer's Almanac, in Detroit, Michigan, the number of hours of sunlight on the summer solstice of 2018 was 15.27, and the number of hours of sunlight on the winter solstice was 9.07.
(a) Find a sinusoidal function of the form
$$
y=A \sin (\omega x-\phi)+B
$$
that models the data.
(b) Use the function found in part (a) to predict the number of hours of sunlight on April 1, the 91st day of the year.
(c) Draw a graph of the function found in part (a).
(d) Look up the number of hours of sunlight for April 1 in the Old Farmer's Almanac, and compare the actual hours of daylight to the results found in part (b).

Ziya Ogron
Ziya Ogron
Numerade Educator
02:46

Problem 33

Graph each function using transformations or the method of key points. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function.

$y=3 \sin x$

Raushan Kumar
Raushan Kumar
Numerade Educator
02:34

Problem 33

Graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function.

$y=2 \cot x-1$

Sheryl Ezze
Sheryl Ezze
Numerade Educator
00:23

Problem 33

Convert each angle in degrees to radians. Express your answer as a multiple of $\pi$.

$-180^{\circ}$

Julie Silva
Julie Silva
Numerade Educator
00:22

Problem 33

Find the exact value of each expression. Do not use a calculator.

$\cos 180^{\circ}-\sin 180^{\circ}$

James Kiss
James Kiss
Numerade Educator
01:12

Problem 33

Name the quadrant in which the angle $\theta$ lies.

$\csc \theta>0, \quad \cos \theta<0$

Harsh Gadhiya
Harsh Gadhiya
Numerade Educator
09:38

Problem 33

According to the Old Farmer's Almanac, in Honolulu, Hawaii, the number of hours of sunlight on the summer solstice of 2018 was 13.42 , and the number of hours of sunlight on the winter solstice was 10.83 .
(a) Find a sinusoidal function of the form
(b) Use the function found in part (a) to predict the number of hours of sunlight on April 1, the 91st day of the year.
(c) Draw a graph of the function found in part (a).
(d) Look up the number of hours of sunlight for April 1 in the Old Farmer's Almanac, and compare the actual hours of daylight to the results found in part (b).

Ziya Ogron
Ziya Ogron
Numerade Educator
02:05

Problem 34

Graph each function using transformations or the method of key points. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function.

$y=4 \cos x$

Micah Hurewitz
Micah Hurewitz
Numerade Educator
05:39

Problem 34

Graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function.

$y=\tan \left(\frac{1}{4} x\right)+1$

David Mccaslin
David Mccaslin
Numerade Educator
00:38

Problem 34

Convert each angle in degrees to radians. Express your answer as a multiple of $\pi$.

$-90^{\circ}$

Julie Silva
Julie Silva
Numerade Educator
00:31

Problem 34

Find the exact value of each expression. Do not use a calculator.

$\sin 90^{\circ}+\tan 45^{\circ}$

James Kiss
James Kiss
Numerade Educator
01:02

Problem 34

Name the quadrant in which the angle $\theta$ lies.

$\sec \theta<0, \quad \sin \theta>0$

Oluwadamilola Ameobi
Oluwadamilola Ameobi
Numerade Educator
09:55

Problem 34

According to the Old Farmer's Almanac, in Anchorage, Alaska, the number of hours of sunlight on the summer solstice of 2018 was 19.37, and the number of hours of sunlight on the winter solstice was 5.45.
(a) Find a sinusoidal function of the form
$$
y=A \sin (\omega x-\phi)+B
$$
that models the data.
(b) Use the function found in part (a) to predict the number of hours of sunlight on April 1, the 91st day of the year.
(c) Draw a graph of the function found in part (a).
(d) Look up the number of hours of sunlight for April 1 in the Old Farmer's Almanac, and compare the actual hours of daylight to the results found in part (b).

Ziya Ogron
Ziya Ogron
Numerade Educator
01:24

Problem 35

Graph each function using transformations or the method of key points. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function.

$y=-4 \sin x$

Raushan Kumar
Raushan Kumar
Numerade Educator
03:40

Problem 35

Graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function.

$y=\csc \left(\frac{3 \pi}{2} x\right)$

David Mccaslin
David Mccaslin
Numerade Educator
01:05

Problem 35

Convert each angle in radians to degrees.

$\frac{\pi}{3}$

Abhijith V
Abhijith V
Numerade Educator
00:30

Problem 35

Find the exact value of each expression. Do not use a calculator.

$\sin 45^{\circ} \cos 45^{\circ}$

James Kiss
James Kiss
Numerade Educator
02:01

Problem 35

$\sin \theta$ and $\cos \theta$ are given. Find the exact value of each of the four remaining trigonometric functions.

$\sin \theta=-\frac{3}{5}, \quad \cos \theta=\frac{4}{5}$

Amit Srivastava
Amit Srivastava
Numerade Educator
06:08

Problem 35

A wooden roller coaster at Six Flags contains a run in the shape of a sinusoidal curve, with a series of hills. The crest of each hill is 106 feet above the ground. If it takes a car 1.8 seconds to go from the top of a hill to the bottom ( 4 feet off the ground), find a sinusoidal function of the form
$$
y=A \sin (\omega t-\phi)+B
$$
that models the motion of the coaster train during this run starting at the top of a hill.
$$
y=A \sin (\omega x-\phi)+B
$$
that models the data.

Ziya Ogron
Ziya Ogron
Numerade Educator
01:23

Problem 36

Graph each function using transformations or the method of key points. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function.

$y=-3 \cos x$

Raushan Kumar
Raushan Kumar
Numerade Educator
02:45

Problem 36

Graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function.

$y=\sec \left(\frac{2 \pi}{3} x\right)+2$

Sheryl Ezze
Sheryl Ezze
Numerade Educator
00:40

Problem 36

Convert each angle in radians to degrees.

$\frac{5 \pi}{6}$

Julie Silva
Julie Silva
Numerade Educator
00:31

Problem 36

Find the exact value of each expression. Do not use a calculator.

$\tan 45^{\circ} \cos 30^{\circ}$

James Kiss
James Kiss
Numerade Educator
01:59

Problem 36

$\sin \theta$ and $\cos \theta$ are given. Find the exact value of each of the four remaining trigonometric functions.

$\sin \theta=\frac{4}{5}, \quad \cos \theta=-\frac{3}{5}$

Amit Srivastava
Amit Srivastava
Numerade Educator
01:40

Problem 36

Explain how the amplitude and period of a sinusoidal graph are used to establish the scale on each coordinate axis.

Micah Hurewitz
Micah Hurewitz
Numerade Educator
02:46

Problem 37

Graph each function using transformations or the method of key points. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function.

$y=\sin (3 x)$

Raushan Kumar
Raushan Kumar
Numerade Educator
05:11

Problem 37

Graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function.

$y=3 \cot \left(\frac{1}{2} x\right)-2$

David Mccaslin
David Mccaslin
Numerade Educator
00:42

Problem 37

Convert each angle in radians to degrees.

$-\frac{2 \pi}{3}$

Julie Silva
Julie Silva
Numerade Educator
00:51

Problem 37

Find the exact value of each expression. Do not use a calculator.

$\sec 30^{\circ} \cot 45^{\circ}$

James Kiss
James Kiss
Numerade Educator
02:23

Problem 37

$\sin \theta$ and $\cos \theta$ are given. Find the exact value of each of the four remaining trigonometric functions.

$\sin \theta=-\frac{\sqrt{5}}{5}, \quad \cos \theta=-\frac{2 \sqrt{5}}{5}$

Amit Srivastava
Amit Srivastava
Numerade Educator
02:32

Problem 37

Find an application in your major field that leads to a sinusoidal graph. Write an account of your findings.

Anjali Kurse
Anjali Kurse
Numerade Educator
02:05

Problem 38

Graph each function using transformations or the method of key points. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function.

$y=\cos (4 x)$

Micah Hurewitz
Micah Hurewitz
Numerade Educator
06:05

Problem 38

Graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function.

$y=\frac{1}{2} \tan \left(\frac{1}{4} x\right)-2$

David Mccaslin
David Mccaslin
Numerade Educator
01:11

Problem 38

Convert each angle in radians to degrees.

$-\frac{13 \pi}{6}$

Abhijith V
Abhijith V
Numerade Educator
01:28

Problem 38

Find the exact value of each expression. Do not use a calculator.

$\csc 45^{\circ} \tan 60^{\circ}$

James Kiss
James Kiss
Numerade Educator
02:08

Problem 38

$\sin \theta$ and $\cos \theta$ are given. Find the exact value of each of the four remaining trigonometric functions.

$\sin \theta=\frac{2 \sqrt{5}}{5}, \quad \cos \theta=\frac{\sqrt{5}}{5}$

Amit Srivastava
Amit Srivastava
Numerade Educator
00:55

Problem 38

Are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

Given $f(x)=\frac{4 x+9}{2}$, find $f^{-1}(x)$.

Ziya Ogron
Ziya Ogron
Numerade Educator
01:37

Problem 39

Graph each function using transformations or the method of key points. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function.

$y=\sin (-2 x)$

Raushan Kumar
Raushan Kumar
Numerade Educator
04:56

Problem 39

Graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function.

$y=3 \sec \left(\frac{1}{4} x\right)+1$

David Mccaslin
David Mccaslin
Numerade Educator
00:31

Problem 39

Convert each angle in radians to degrees.

$4 \pi$

Julie Silva
Julie Silva
Numerade Educator
00:37

Problem 39

Find the exact value of each expression. Do not use a calculator.

$5 \cos 90^{\circ}-8 \sin 270^{\circ}$

James Kiss
James Kiss
Numerade Educator
02:05

Problem 39

$\sin \theta$ and $\cos \theta$ are given. Find the exact value of each of the four remaining trigonometric functions.

$\sin \theta=\frac{\sqrt{3}}{2}, \quad \cos \theta=\frac{1}{2}$

Amit Srivastava
Amit Srivastava
Numerade Educator
01:00

Problem 39

Are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

Solve: $0.25(0.4 x+0.8)=3.7-1.4 x$

Ziya Ogron
Ziya Ogron
Numerade Educator
01:41

Problem 40

Graph each function using transformations or the method of key points. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function.

$y=\cos (-2 x)$

Raushan Kumar
Raushan Kumar
Numerade Educator
05:03

Problem 40

Graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function.

$y=2 \csc \left(\frac{1}{3} x\right)-1$

David Mccaslin
David Mccaslin
Numerade Educator
01:05

Problem 40

Convert each angle in radians to degrees.

$\frac{9 \pi}{2}$

Abhijith V
Abhijith V
Numerade Educator
00:45

Problem 40

Find the exact value of each expression. Do not use a calculator.

$4 \sin 90^{\circ}-3 \tan 180^{\circ}$

James Kiss
James Kiss
Numerade Educator
01:59

Problem 40

$\sin \theta$ and $\cos \theta$ are given. Find the exact value of each of the four remaining trigonometric functions.

$\sin \theta=\frac{1}{2}, \quad \cos \theta=\frac{\sqrt{3}}{2}$

Amit Srivastava
Amit Srivastava
Numerade Educator
01:01

Problem 40

Are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

Multiply: $(8 x+15 y)^2$

Ziya Ogron
Ziya Ogron
Numerade Educator
01:27

Problem 41

Graph each function using transformations or the method of key points. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function.

$y=2 \cos \left(\frac{1}{4} x\right)$

Raushan Kumar
Raushan Kumar
Numerade Educator
02:31

Problem 41

Find the average rate of change of from 0 to $\frac{\pi}{6}$.

$f(x)=\sec x$

David Mccaslin
David Mccaslin
Numerade Educator
00:38

Problem 41

Convert each angle in radians to degrees.

$\frac{5 \pi}{12}$

Julie Silva
Julie Silva
Numerade Educator
01:10

Problem 41

Find the exact value of each expression. Do not use a calculator.

$2 \sin \frac{\pi}{3}-3 \tan \frac{\pi}{6}$

James Kiss
James Kiss
Numerade Educator
02:18

Problem 41

$\sin \theta$ and $\cos \theta$ are given. Find the exact value of each of the four remaining trigonometric functions.

$\sin \theta=\frac{2 \sqrt{2}}{3}, \quad \cos \theta=-\frac{1}{3}$

Amit Srivastava
Amit Srivastava
Numerade Educator
01:30

Problem 41

Are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

Find the exact distance between the points $(4,-1)$ and $(10,3)$.

Ziya Ogron
Ziya Ogron
Numerade Educator
01:24

Problem 42

Graph each function using transformations or the method of key points. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function.

$y=2 \sin \left(\frac{1}{2} x\right)$

Raushan Kumar
Raushan Kumar
Numerade Educator
01:54

Problem 42

Find the average rate of change of from 0 to $\frac{\pi}{6}$.

$f(x)=\tan x$

David Mccaslin
David Mccaslin
Numerade Educator
01:07

Problem 42

Convert each angle in radians to degrees.

$\frac{3 \pi}{20}$

Abhijith V
Abhijith V
Numerade Educator
01:02

Problem 42

Find the exact value of each expression. Do not use a calculator.

$2 \sin \frac{\pi}{4}+3 \tan \frac{\pi}{4}$

James Kiss
James Kiss
Numerade Educator
02:40

Problem 42

$\sin \theta$ and $\cos \theta$ are given. Find the exact value of each of the four remaining trigonometric functions.

$\sin \theta=-\frac{1}{3}, \quad \cos \theta=\frac{2 \sqrt{2}}{3}$

Amit Srivastava
Amit Srivastava
Numerade Educator
01:55

Problem 42

Are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

Solve: $|3 x+4|=|5 x-7|$

Ziya Ogron
Ziya Ogron
Numerade Educator
01:30

Problem 43

Graph each function using transformations or the method of key points. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function.

$y=-\frac{1}{2} \cos (2 x)$

Raushan Kumar
Raushan Kumar
Numerade Educator
01:56

Problem 43

Find the average rate of change of from 0 to $\frac{\pi}{6}$.

$f(x)=\sec (2 x)$

David Mccaslin
David Mccaslin
Numerade Educator
00:30

Problem 43

Convert each angle in radians to degrees.

$-\pi$

Julie Silva
Julie Silva
Numerade Educator
01:04

Problem 43

Find the exact value of each expression. Do not use a calculator.

$3 \csc \frac{\pi}{3}+\cot \frac{\pi}{4}$

James Kiss
James Kiss
Numerade Educator
02:50

Problem 43

Find the exact value of each of the remaining trigonometric functions of $\theta$.

$\sin \theta=\frac{12}{13}, \quad \theta$ in quadrant II

Amit Srivastava
Amit Srivastava
Numerade Educator
01:37

Problem 43

Are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

Given $y=x \sqrt{x+4}$, let $u=x+4$ and express $y$ in terms of $u$.

Ziya Ogron
Ziya Ogron
Numerade Educator
01:33

Problem 44

Graph each function using transformations or the method of key points. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function.

$y=-4 \sin \left(\frac{1}{8} x\right)$

Raushan Kumar
Raushan Kumar
Numerade Educator
02:15

Problem 44

Find the average rate of change of from 0 to $\frac{\pi}{6}$.

$f(x)=\tan (2 x)$

David Mccaslin
David Mccaslin
Numerade Educator
00:34

Problem 44

Convert each angle in radians to degrees.

$-\frac{\pi}{2}$

Julie Silva
Julie Silva
Numerade Educator
01:49

Problem 44

Find the exact value of each expression. Do not use a calculator.

$2 \sec \frac{\pi}{4}+4 \cot \frac{\pi}{3}$

James Kiss
James Kiss
Numerade Educator
02:45

Problem 44

Find the exact value of each of the remaining trigonometric functions of $\theta$.

$\cos \theta=\frac{3}{5}, \quad \theta$ in quadrant IV

Urjeet Deshmukh
Urjeet Deshmukh
Numerade Educator
02:16

Problem 44

Are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

If $x=a \sin t, a>0$, and $-\frac{\pi}{2} \leq t \leq \frac{\pi}{2}$, find $\cos t$.

Ziya Ogron
Ziya Ogron
Numerade Educator
02:21

Problem 45

Graph each function using transformations or the method of key points. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function.

$y=3 \cos x+2$

Raushan Kumar
Raushan Kumar
Numerade Educator
04:43

Problem 45

$$
\text { Find }(f \circ g)(x) \text { and }(g \circ f)(x) \text {, and graph each of these functions. }
$$
$$
\text { } \begin{aligned}
f(x) & =2 \sec x \\
g(x) & =\frac{1}{2} x
\end{aligned}
$$

David Mccaslin
David Mccaslin
Numerade Educator
00:43

Problem 45

Convert each angle in radians to degrees.

$-\frac{3 \pi}{4}$

Julie Silva
Julie Silva
Numerade Educator
00:47

Problem 45

Find the exact value of each expression. Do not use a calculator.

$\sec \pi-\csc \frac{\pi}{2}$

James Kiss
James Kiss
Numerade Educator
02:54

Problem 45

Find the exact value of each of the remaining trigonometric functions of $\theta$.

$\sin \theta=-\frac{5}{13}, \quad \theta$ in quadrant III

Urjeet Deshmukh
Urjeet Deshmukh
Numerade Educator
02:02

Problem 45

Are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

A rectangular garden is enclosed by 54 feet of fencing. If the length of the garden is 3 feet more than twice the width, what are the dimensions of the garden?

Ziya Ogron
Ziya Ogron
Numerade Educator
02:46

Problem 46

Graph each function using transformations or the method of key points. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function.

$y=2 \sin x+3$

Raushan Kumar
Raushan Kumar
Numerade Educator
03:33

Problem 46

$$
\text { Find }(f \circ g)(x) \text { and }(g \circ f)(x) \text {, and graph each of these functions. }
$$

$$
\text { } \begin{aligned}
& f(x)=\tan x \\
& g(x)=4 x
\end{aligned}
$$

David Mccaslin
David Mccaslin
Numerade Educator
01:12

Problem 46

Convert each angle in radians to degrees.

$-\frac{17 \pi}{15}$

Abhijith V
Abhijith V
Numerade Educator
00:47

Problem 46

Find the exact value of each expression. Do not use a calculator.

$\csc \frac{\pi}{2}+\cot \frac{\pi}{2}$

James Kiss
James Kiss
Numerade Educator
02:45

Problem 46

Find the exact value of each of the remaining trigonometric functions of $\theta$.

$\cos \theta=-\frac{4}{5}, \quad \theta$ in quadrant III

Urjeet Deshmukh
Urjeet Deshmukh
Numerade Educator
01:23

Problem 46

Are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

Find the vertical asymptotes, if any, of the graph of $R(x)=\frac{x^2-25}{x^2-2 x-15}$.

Ziya Ogron
Ziya Ogron
Numerade Educator
02:29

Problem 47

Graph each function using transformations or the method of key points. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function.

$y=4 \sin \left(\frac{\pi}{2} x\right)-2$

Raushan Kumar
Raushan Kumar
Numerade Educator
03:56

Problem 47

$$
\text { Find }(f \circ g)(x) \text { and }(g \circ f)(x) \text {, and graph each of these functions. }
$$

$$
\text { } \begin{aligned}
f(x) & =\frac{1}{2} x \\
g(x) & =2 \csc x
\end{aligned}
$$

David Mccaslin
David Mccaslin
Numerade Educator
00:46

Problem 47

Convert each angle in degrees to radians. Express your answer in decimal form, rounded to two decimal places.

$73^{\circ}$

Julie Silva
Julie Silva
Numerade Educator
02:35

Problem 47

Find the exact values of the six trigonometric functions of the given angle. If any are not defined, say "not defined." Do not use a calculator.

$\frac{2 \pi}{3}$

NA
Natasha Antonini
Numerade Educator
02:59

Problem 47

Find the exact value of each of the remaining trigonometric functions of $\theta$.

$\cos \theta=\frac{4}{5}, \quad 270^{\circ}<\theta<360^{\circ}$

Urjeet Deshmukh
Urjeet Deshmukh
Numerade Educator
01:00

Problem 47

Are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

Write $\log _2\left(8 x^2 y^5\right)$ as a sum of logarithms. Express powers as factors.

Ziya Ogron
Ziya Ogron
Numerade Educator
02:53

Problem 48

Graph each function using transformations or the method of key points. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function.

$y=5 \cos (\pi x)-3$

Raushan Kumar
Raushan Kumar
Numerade Educator
06:04

Problem 48

$$
\text { Find }(f \circ g)(x) \text { and }(g \circ f)(x) \text {, and graph each of these functions. }
$$

$$
\begin{aligned}
& f(x)=-2 x \\
& g(x)=\cot x
\end{aligned}
$$

David Mccaslin
David Mccaslin
Numerade Educator
00:50

Problem 48

Convert each angle in degrees to radians. Express your answer in decimal form, rounded to two decimal places.

$17^{\circ}$

Julie Silva
Julie Silva
Numerade Educator
02:05

Problem 48

Find the exact values of the six trigonometric functions of the given angle. If any are not defined, say "not defined." Do not use a calculator.

$\frac{5 \pi}{6}$

James Kiss
James Kiss
Numerade Educator
03:03

Problem 48

Find the exact value of each of the remaining trigonometric functions of $\theta$.

$\sin \theta=\frac{5}{13}, 90^{\circ}<\theta<180^{\circ}$

Urjeet Deshmukh
Urjeet Deshmukh
Numerade Educator
02:33

Problem 49

Graph each function using transformations or the method of key points. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function.

$y=-6 \sin \left(\frac{\pi}{3} x\right)+4$

Raushan Kumar
Raushan Kumar
Numerade Educator
03:20

Problem 49

Graph each function.
$$
\text { } g(x)= \begin{cases}\csc x & \text { if } 0<x<\pi \\ 0 & \text { if } x=\pi \\ \cot x & \text { if } \pi<x<2 \pi\end{cases}
$$

David Mccaslin
David Mccaslin
Numerade Educator
00:48

Problem 49

Convert each angle in degrees to radians. Express your answer in decimal form, rounded to two decimal places.

$-40^{\circ}$

Julie Silva
Julie Silva
Numerade Educator
02:01

Problem 49

Find the exact values of the six trigonometric functions of the given angle. If any are not defined, say "not defined." Do not use a calculator.

$240^{\circ}$

James Kiss
James Kiss
Numerade Educator
03:18

Problem 49

Find the exact value of each of the remaining trigonometric functions of $\theta$.

$\sin \theta=-\frac{2}{3}, \quad \pi<\theta<\frac{3 \pi}{2}$

Amit Srivastava
Amit Srivastava
Numerade Educator
02:07

Problem 50

Graph each function using transformations or the method of key points. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function.

$y=-3 \cos \left(\frac{\pi}{4} x\right)+2$

Raushan Kumar
Raushan Kumar
Numerade Educator
03:10

Problem 50

Graph each function.
$$
f(x)= \begin{cases}\tan x & \text { if } 0 \leq x<\frac{\pi}{2} \\ 0 & \text { if } x=\frac{\pi}{2} \\ \sec x & \text { if } \frac{\pi}{2}<x \leq \pi\end{cases}
$$

David Mccaslin
David Mccaslin
Numerade Educator
00:49

Problem 50

Convert each angle in degrees to radians. Express your answer in decimal form, rounded to two decimal places.

$-51^{\circ}$

Julie Silva
Julie Silva
Numerade Educator
01:34

Problem 50

Find the exact values of the six trigonometric functions of the given angle. If any are not defined, say "not defined." Do not use a calculator.

$210^{\circ}$

James Kiss
James Kiss
Numerade Educator
03:01

Problem 50

Find the exact value of each of the remaining trigonometric functions of $\theta$.

$\cos \theta=-\frac{1}{3}, \quad \frac{\pi}{2}<\theta<\pi$

Amit Srivastava
Amit Srivastava
Numerade Educator
02:07

Problem 51

Graph each function using transformations or the method of key points. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function.

$y=2-4 \cos (3 x)$

Raushan Kumar
Raushan Kumar
Numerade Educator
06:49

Problem 51

Two hallways, one of width 3 feet, the other of width 4 feet, meet at a right angle. See the figure.FIGURE CANT COPY

(a) Show that the length $L$ of the ladder shown as a function of the angle $\theta$ is
$$
L(\theta)=3 \sec \theta+4 \csc \theta
$$
(b) Graph $L=L(\theta), 0<\theta<\frac{\pi}{2}$.
(c) For what value of $\theta$ is $L$ the least?
(d) What is the length of the longest ladder that can be carried around the corner? Why is this also the least value of $L$ ?

David Mccaslin
David Mccaslin
Numerade Educator
00:49

Problem 51

Convert each angle in degrees to radians. Express your answer in decimal form, rounded to two decimal places.

$350^{\circ}$

Julie Silva
Julie Silva
Numerade Educator
01:24

Problem 51

Find the exact values of the six trigonometric functions of the given angle. If any are not defined, say "not defined." Do not use a calculator.

$\frac{3 \pi}{4}$

James Kiss
James Kiss
Numerade Educator
03:44

Problem 51

Find the exact value of each of the remaining trigonometric functions of $\theta$.

$\cos \theta=-\frac{1}{4}, \quad \tan \theta>0$

Urjeet Deshmukh
Urjeet Deshmukh
Numerade Educator
02:18

Problem 52

Graph each function using transformations or the method of key points. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function.

$y=5-3 \sin (2 x)$

Raushan Kumar
Raushan Kumar
Numerade Educator
00:55

Problem 52

Convert each angle in degrees to radians. Express your answer in decimal form, rounded to two decimal places.

$125^{\circ}$

Julie Silva
Julie Silva
Numerade Educator
01:32

Problem 52

Find the exact values of the six trigonometric functions of the given angle. If any are not defined, say "not defined." Do not use a calculator.

$\frac{11 \pi}{4}$

James Kiss
James Kiss
Numerade Educator
03:30

Problem 52

Find the exact value of each of the remaining trigonometric functions of $\theta$.

$\sin \theta=\frac{2}{3}, \quad \tan \theta<0$

Urjeet Deshmukh
Urjeet Deshmukh
Numerade Educator
01:52

Problem 53

Graph each function using transformations or the method of key points. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function.

$y=\frac{9}{5} \cos \left(-\frac{3 \pi}{2} x\right)$

Raushan Kumar
Raushan Kumar
Numerade Educator
04:02

Problem 53

Graph
$$
y=\tan x \text { and } y=-\cot \left(x+\frac{\pi}{2}\right)
$$
Do you think that $\tan x=-\cot \left(x+\frac{\pi}{2}\right)$ ?

David Mccaslin
David Mccaslin
Numerade Educator
01:22

Problem 53

Convert each angle in radians to degrees. Express your answer in decimal form, rounded to two decimal places.

0.75

Abhijith V
Abhijith V
Numerade Educator
01:37

Problem 53

Find the exact values of the six trigonometric functions of the given angle. If any are not defined, say "not defined." Do not use a calculator.

$\frac{13 \pi}{6}$

James Kiss
James Kiss
Numerade Educator
03:18

Problem 53

Find the exact value of each of the remaining trigonometric functions of $\theta$.

$\csc \theta=3, \quad \cot \theta<0$

Amit Srivastava
Amit Srivastava
Numerade Educator
02:11

Problem 54

Graph each function using transformations or the method of key points. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function.

$y=\frac{5}{3} \sin \left(-\frac{2 \pi}{3} x\right)$

Raushan Kumar
Raushan Kumar
Numerade Educator
02:28

Problem 54

Suppose that a fire truck is parked in front of a building as shown in the figure.

The beacon light on top of the fire truck is located 10 feet from the wall and has a light on each side. If the beacon light rotates 1 revolution every 2 seconds, then a model for determining the distance $d$, in feet, that the beacon of light is from point $A$ on the wall after $t$ seconds is given by
$$
d(t)=|10 \tan (\pi t)|
$$
(a) Graph $d(t)=|10 \tan (\pi t)|$ for $0 \leq t \leq 2$.
(b) For what values of $t$ is the function undefined? Explain what this means in terms of the beam of light on the wall.
(c) Fill in the following table.
$$
\begin{array}{|l|l|l|l|l|l|}
\hline t & 0 & 0.1 & 0.2 & 0.3 & 0.4 \\
\hline d(t)=10 \tan (\pi t) & & & & & \\
\hline
\end{array}
$$
(d) Compute $\frac{d(0.1)-d(0)}{0.1-0}, \frac{d(0.2)-d(0.1)}{0.2-0.1}$, and so on, for each consecutive value of $t$. These are called first differences.
(e) Interpret the first differences found in part (d). What is happening to the speed of the beam of light as $d$ increases?

Yuou Sun
Yuou Sun
Numerade Educator
02:42

Problem 54

What are the domain and the range of $f(x)=\log (\tan x)$ ? Find any vertical asymptotes.

Yujie Wang
Yujie Wang
College of San Mateo
01:27

Problem 54

Convert each angle in radians to degrees. Express your answer in decimal form, rounded to two decimal places.

3.14

Abhijith V
Abhijith V
Numerade Educator
01:42

Problem 54

Find the exact values of the six trigonometric functions of the given angle. If any are not defined, say "not defined." Do not use a calculator.

$\frac{8 \pi}{3}$

James Kiss
James Kiss
Numerade Educator
03:10

Problem 54

Find the exact value of each of the remaining trigonometric functions of $\theta$.

$\sec \theta=2, \quad \sin \theta<0$

Amit Srivastava
Amit Srivastava
Numerade Educator
02:02

Problem 55

Graph each function using transformations or the method of key points. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function.

$y=-\frac{1}{2} \sin \left(\frac{\pi}{8} x\right)+\frac{3}{2}$

Raushan Kumar
Raushan Kumar
Numerade Educator
02:34

Problem 55

What are the domain and the range of $f(x)=\ln |\sin x|$ ? Find any vertical asymptotes.

Yujie Wang
Yujie Wang
College of San Mateo
00:52

Problem 55

Convert each angle in radians to degrees. Express your answer in decimal form, rounded to two decimal places.

3

Julie Silva
Julie Silva
Numerade Educator
01:32

Problem 55

Find the exact values of the six trigonometric functions of the given angle. If any are not defined, say "not defined." Do not use a calculator.

$405^{\circ}$

James Kiss
James Kiss
Numerade Educator
02:43

Problem 55

Find the exact value of each of the remaining trigonometric functions of $\theta$.

$\cot \theta=\frac{4}{3}, \quad \cos \theta<0$

Amit Srivastava
Amit Srivastava
Numerade Educator
02:41

Problem 56

Graph each function using transformations or the method of key points. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function.

$y=-\frac{3}{2} \cos \left(\frac{\pi}{4} x\right)+\frac{1}{2}$

Raushan Kumar
Raushan Kumar
Numerade Educator
02:11

Problem 56

Problems are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

Factor: $125 p^3-8 q^6$

Yujie Wang
Yujie Wang
College of San Mateo
01:04

Problem 56

Convert each angle in radians to degrees. Express your answer in decimal form, rounded to two decimal places.

7

Abhijith V
Abhijith V
Numerade Educator
01:36

Problem 56

Find the exact values of the six trigonometric functions of the given angle. If any are not defined, say "not defined." Do not use a calculator.

$390^{\circ}$

James Kiss
James Kiss
Numerade Educator
02:41

Problem 56

Find the exact value of each of the remaining trigonometric functions of $\theta$.

$\tan \theta=\frac{3}{4}, \quad \sin \theta<0$

Amit Srivastava
Amit Srivastava
Numerade Educator
01:29

Problem 57

Write the equation of a sine function that has the given characteristics.

Amplitude: 3
Period: $\pi$

Micah Hurewitz
Micah Hurewitz
Numerade Educator
04:36

Problem 57

Problems are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

Painting a Room Hazel can paint a room in 2 hours less time than her friend Gwyneth. Working together, they can paint the room in 2.4 hours. How long does it take each woman to paint the room by herself?

Yujie Wang
Yujie Wang
College of San Mateo
00:54

Problem 57

Convert each angle in radians to degrees. Express your answer in decimal form, rounded to two decimal places.

$\sqrt{2}$

Julie Silva
Julie Silva
Numerade Educator
01:26

Problem 57

Find the exact values of the six trigonometric functions of the given angle. If any are not defined, say "not defined." Do not use a calculator.

$-\frac{\pi}{3}$

James Kiss
James Kiss
Numerade Educator
03:14

Problem 57

Find the exact value of each of the remaining trigonometric functions of $\theta$.

$\sec \theta=-2, \quad \tan \theta>0$

Urjeet Deshmukh
Urjeet Deshmukh
Numerade Educator
01:32

Problem 58

Write the equation of a sine function that has the given characteristics.

Amplitude: 2
Period: $4 \pi$

Micah Hurewitz
Micah Hurewitz
Numerade Educator
00:46

Problem 58

Problems are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

Solve: $9^{x-1}=3^{x^2-5}$

Yujie Wang
Yujie Wang
College of San Mateo
01:18

Problem 58

Convert each angle in radians to degrees. Express your answer in decimal form, rounded to two decimal places.

9.28

Abhijith V
Abhijith V
Numerade Educator
01:45

Problem 58

Find the exact values of the six trigonometric functions of the given angle. If any are not defined, say "not defined." Do not use a calculator.

$-\frac{\pi}{6}$

James Kiss
James Kiss
Numerade Educator
02:36

Problem 58

Find the exact value of each of the remaining trigonometric functions of $\theta$.

$\tan \theta=-\frac{1}{3}, \quad \sin \theta>0$

AG
Ankit Gupta
Numerade Educator
01:46

Problem 59

Write the equation of a sine function that has the given characteristics.

Amplitude: 4
Period: 1

Micah Hurewitz
Micah Hurewitz
Numerade Educator
01:40

Problem 59

Problems are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

Use the slope and the $y$-intercept to graph the linear function
$$
f(x)=\frac{1}{4} x-3
$$

Yujie Wang
Yujie Wang
College of San Mateo
01:57

Problem 59

Convert each angle to a decimal in degrees. Round your answer to two decimal places.

$40^{\circ} 10^{\prime} 25^{\prime \prime}$

Julie Silva
Julie Silva
Numerade Educator
01:47

Problem 59

Find the exact values of the six trigonometric functions of the given angle. If any are not defined, say "not defined." Do not use a calculator.

$-240^{\circ}$

James Kiss
James Kiss
Numerade Educator
00:34

Problem 59

Use the even-odd properties to find the exact value of each expression. Do not use a calculator.

$\sin \left(-60^{\circ}\right)$

Amit Srivastava
Amit Srivastava
Numerade Educator
01:40

Problem 60

Write the equation of a sine function that has the given characteristics.

Amplitude: 3
Period: 2

Micah Hurewitz
Micah Hurewitz
Numerade Educator
01:20

Problem 60

Problems are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

Find the domain of $y=\log _4\left(\frac{x-4}{x}\right)$.

Yujie Wang
Yujie Wang
College of San Mateo
01:52

Problem 60

Convert each angle to a decimal in degrees. Round your answer to two decimal places.

$61^{\circ} 42^{\prime} 21^{\prime \prime}$

Julie Silva
Julie Silva
Numerade Educator
01:30

Problem 60

Find the exact values of the six trigonometric functions of the given angle. If any are not defined, say "not defined." Do not use a calculator.

$-135^{\circ}$

James Kiss
James Kiss
Numerade Educator
00:44

Problem 60

Use the even-odd properties to find the exact value of each expression. Do not use a calculator.

$\cos \left(-30^{\circ}\right)$

Amit Srivastava
Amit Srivastava
Numerade Educator

Problem 61

Find an equation for each graph.

(GRAPH CANT COPY)

Check back soon!
02:12

Problem 61

Problems are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

If $f(x)=\frac{x+1}{x-2}$ and $g(x)=3 x-7$, find $(g \circ f)(3)$.

Yujie Wang
Yujie Wang
College of San Mateo
01:48

Problem 61

Convert each angle to a decimal in degrees. Round your answer to two decimal places.

$73^{\circ} 40^{\prime} 40^{\prime \prime}$

Julie Silva
Julie Silva
Numerade Educator
01:59

Problem 61

Find the exact values of the six trigonometric functions of the given angle. If any are not defined, say "not defined." Do not use a calculator.

$\frac{5 \pi}{2}$

James Kiss
James Kiss
Numerade Educator
00:42

Problem 61

Use the even-odd properties to find the exact value of each expression. Do not use a calculator.

$\sin \left(-135^{\circ}\right)$

Amit Srivastava
Amit Srivastava
Numerade Educator

Problem 62

Find an equation for each graph.

(GRAPH CANT COPY)

Check back soon!
01:43

Problem 62

Problems are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

If $f(x)=x^2-3 x$, find $\frac{f(x)-f(c)}{x-c}$.

Yujie Wang
Yujie Wang
College of San Mateo
01:59

Problem 62

Convert each angle to a decimal in degrees. Round your answer to two decimal places.

$50^{\circ} 14^{\prime} 20^{\prime \prime}$

Abhijith V
Abhijith V
Numerade Educator
01:29

Problem 62

Find the exact values of the six trigonometric functions of the given angle. If any are not defined, say "not defined." Do not use a calculator.

$5 \pi$

James Kiss
James Kiss
Numerade Educator
00:47

Problem 62

Use the even-odd properties to find the exact value of each expression. Do not use a calculator.

$\tan \left(-30^{\circ}\right)$

Amit Srivastava
Amit Srivastava
Numerade Educator

Problem 63

Find an equation for each graph.

(GRAPH CANT COPY)

Check back soon!
02:39

Problem 63

Problems are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

Find the intercepts of the graph of the function
$$
f(x)=\frac{2 x^2+x-6}{x+3}
$$

Yujie Wang
Yujie Wang
College of San Mateo
01:51

Problem 63

Convert each angle to a decimal in degrees. Round your answer to two decimal places.

$98^{\circ} 22^{\prime} 45^{\prime \prime}$

Julie Silva
Julie Silva
Numerade Educator
02:11

Problem 63

Find the exact values of the six trigonometric functions of the given angle. If any are not defined, say "not defined." Do not use a calculator.

$-\frac{13 \pi}{6}$

James Kiss
James Kiss
Numerade Educator
00:53

Problem 63

Use the even-odd properties to find the exact value of each expression. Do not use a calculator.

$\csc \left(-30^{\circ}\right)$

Amit Srivastava
Amit Srivastava
Numerade Educator

Problem 64

Find an equation for each graph.

(GRAPH CANT COPY)

Check back soon!
01:02

Problem 64

Problems are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

Complete the square in $x$ to write $\sqrt{x^2+2 x+26}$ in the form $\sqrt{u^2+a^2}$.

Yujie Wang
Yujie Wang
College of San Mateo
01:46

Problem 64

Convert each angle to a decimal in degrees. Round your answer to two decimal places.

$9^{\circ} 9^{\prime} 9^{\prime \prime}$

Julie Silva
Julie Silva
Numerade Educator
02:41

Problem 64

Find the exact values of the six trigonometric functions of the given angle. If any are not defined, say "not defined." Do not use a calculator.

$-\frac{14 \pi}{3}$

James Kiss
James Kiss
Numerade Educator
00:45

Problem 64

Use the even-odd properties to find the exact value of each expression. Do not use a calculator.

$\sec \left(-60^{\circ}\right)$

Amit Srivastava
Amit Srivastava
Numerade Educator

Problem 65

Find an equation for each graph.

(GRAPH CANT COPY)

Check back soon!
01:49

Problem 65

Convert each angle to $D^{\circ} M^{\prime} S^{\prime \prime}$ form. Round your answer to the nearest second.

$40.32^{\circ}$

Julie Silva
Julie Silva
Numerade Educator
00:30

Problem 65

Use a calculator to find the approximate value of each expression rounded to two decimal places.

$\sin 28^{\circ}$

James Kiss
James Kiss
Numerade Educator
00:42

Problem 65

Use the even-odd properties to find the exact value of each expression. Do not use a calculator.

$\cos \left(-270^{\circ}\right)$

Amit Srivastava
Amit Srivastava
Numerade Educator

Problem 66

Find an equation for each graph.

(GRAPH CANT COPY)

Check back soon!
01:53

Problem 66

Convert each angle to $D^{\circ} M^{\prime} S^{\prime \prime}$ form. Round your answer to the nearest second.

$61.24^{\circ}$

Julie Silva
Julie Silva
Numerade Educator
00:24

Problem 66

Use a calculator to find the approximate value of each expression rounded to two decimal places.

$\cos 14^{\circ}$

James Kiss
James Kiss
Numerade Educator
00:32

Problem 66

Use the even-odd properties to find the exact value of each expression. Do not use a calculator.

$\sin \left(-90^{\circ}\right)$

Amit Srivastava
Amit Srivastava
Numerade Educator

Problem 67

Find an equation for each graph.

(GRAPH CANT COPY)

Check back soon!
02:13

Problem 67

Convert each angle to $D^{\circ} M^{\prime} S^{\prime \prime}$ form. Round your answer to the nearest second.

$29.411^{\prime \prime}$

Julie Silva
Julie Silva
Numerade Educator
00:35

Problem 67

Use a calculator to find the approximate value of each expression rounded to two decimal places.

$\cot 70^{\circ}$

James Kiss
James Kiss
Numerade Educator
00:35

Problem 67

Use the even-odd properties to find the exact value of each expression. Do not use a calculator.

$\sin (-\pi)$

Amit Srivastava
Amit Srivastava
Numerade Educator

Problem 68

Find an equation for each graph.

(GRAPH CANT COPY)

Check back soon!
01:45

Problem 68

Convert each angle to $D^{\circ} M^{\prime} S^{\prime \prime}$ form. Round your answer to the nearest second.

$18.255^{\circ}$

Julie Silva
Julie Silva
Numerade Educator
00:37

Problem 68

Use a calculator to find the approximate value of each expression rounded to two decimal places.

$\sec 21^{\circ}$

James Kiss
James Kiss
Numerade Educator
00:41

Problem 68

Use the even-odd properties to find the exact value of each expression. Do not use a calculator.

$\tan \left(-\frac{\pi}{4}\right)$

Amit Srivastava
Amit Srivastava
Numerade Educator

Problem 69

Find an equation for each graph.

(GRAPH CANT COPY)

Check back soon!
01:47

Problem 69

Convert each angle to $D^{\circ} M^{\prime} S^{\prime \prime}$ form. Round your answer to the nearest second.

$44.01^{\circ}$

Julie Silva
Julie Silva
Numerade Educator
00:57

Problem 69

Use a calculator to find the approximate value of each expression rounded to two decimal places.

$\sin \frac{\pi}{8}$

James Kiss
James Kiss
Numerade Educator
00:45

Problem 69

Use the even-odd properties to find the exact value of each expression. Do not use a calculator.

$\sin \left(-\frac{\pi}{3}\right)$

Amit Srivastava
Amit Srivastava
Numerade Educator

Problem 70

Find an equation for each graph.

(GRAPH CANT COPY)

Check back soon!
01:41

Problem 70

Convert each angle to $D^{\circ} M^{\prime} S^{\prime \prime}$ form. Round your answer to the nearest second.

$19.99^{\circ}$

Julie Silva
Julie Silva
Numerade Educator
00:50

Problem 70

Use a calculator to find the approximate value of each expression rounded to two decimal places.

$\tan \frac{\pi}{10}$

James Kiss
James Kiss
Numerade Educator
00:41

Problem 70

Use the even-odd properties to find the exact value of each expression. Do not use a calculator.

$\cos \left(-\frac{\pi}{4}\right)$

Amit Srivastava
Amit Srivastava
Numerade Educator

Problem 71

Find an equation for each graph.

(GRAPH CANT COPY)

Check back soon!
01:08

Problem 71

S denotes the length of the arc of a circle of radius $r$ subtended by the central angle $\theta$. Find the missing quantity. Round answers to three decimal places.

$r=10$ meters, $\theta=\frac{1}{2}$ radian, $s=$ ?

Abhijith V
Abhijith V
Numerade Educator
00:57

Problem 71

Use a calculator to find the approximate value of each expression rounded to two decimal places.

$\csc \frac{5 \pi}{13}$

James Kiss
James Kiss
Numerade Educator
00:52

Problem 71

Use the even-odd properties to find the exact value of each expression. Do not use a calculator.

$\sin \left(-\frac{3 \pi}{2}\right)$

Amit Srivastava
Amit Srivastava
Numerade Educator

Problem 72

Find an equation for each graph.

(GRAPH CANT COPY)

Check back soon!
01:07

Problem 72

S denotes the length of the arc of a circle of radius $r$ subtended by the central angle $\theta$. Find the missing quantity. Round answers to three decimal places.

$r=6$ feet, $\theta=2$ radians, $s=$ ?

Abhijith V
Abhijith V
Numerade Educator
00:48

Problem 72

Use a calculator to find the approximate value of each expression rounded to two decimal places.

$\cot \frac{\pi}{12}$

James Kiss
James Kiss
Numerade Educator
00:45

Problem 72

Use the even-odd properties to find the exact value of each expression. Do not use a calculator.

$\tan (-\pi)$

Amit Srivastava
Amit Srivastava
Numerade Educator

Problem 73

Find an equation for each graph.

(GRAPH CANT COPY)

Check back soon!
01:06

Problem 73

S denotes the length of the arc of a circle of radius $r$ subtended by the central angle $\theta$. Find the missing quantity. Round answers to three decimal places.

$\theta=\frac{1}{4}$ radian, $s=6$ centimeters, $r=$ ?

Dharmendra Jain
Dharmendra Jain
Numerade Educator
00:27

Problem 73

Use a calculator to find the approximate value of each expression rounded to two decimal places.

$\tan 1$

Ethan Somes
Ethan Somes
Numerade Educator
00:43

Problem 73

Use the even-odd properties to find the exact value of each expression. Do not use a calculator.

$\sec (-\pi)$

Amit Srivastava
Amit Srivastava
Numerade Educator

Problem 74

Find an equation for each graph.

(GRAPH CANT COPY)

Check back soon!
01:19

Problem 74

S denotes the length of the arc of a circle of radius $r$ subtended by the central angle $\theta$. Find the missing quantity. Round answers to three decimal places.

$\theta=\frac{2}{3}$ radian, $s=8$ feet, $r=$ ?

Abhijith V
Abhijith V
Numerade Educator
00:36

Problem 74

Use a calculator to find the approximate value of each expression rounded to two decimal places.

$\sin 1$

Ethan Somes
Ethan Somes
Numerade Educator
00:59

Problem 74

Use the even-odd properties to find the exact value of each expression. Do not use a calculator.

$\csc \left(-\frac{\pi}{4}\right)$

Amit Srivastava
Amit Srivastava
Numerade Educator
01:16

Problem 75

Find the average rate of change of from 0 to $\frac{\pi}{2}$.

$f(x)=\cos x$

Micah Hurewitz
Micah Hurewitz
Numerade Educator
01:12

Problem 75

S denotes the length of the arc of a circle of radius $r$ subtended by the central angle $\theta$. Find the missing quantity. Round answers to three decimal places.

$r=6$ meters, $s=8$ meters, $\theta=$ ?

Abhijith V
Abhijith V
Numerade Educator
00:31

Problem 75

Use a calculator to find the approximate value of each expression rounded to two decimal places.

$\tan 1^{\circ}$

Ethan Somes
Ethan Somes
Numerade Educator
01:01

Problem 75

Use the even-odd properties to find the exact value of each expression. Do not use a calculator.

$\csc \left(-\frac{\pi}{3}\right)$

Amit Srivastava
Amit Srivastava
Numerade Educator
01:27

Problem 76

Find the average rate of change of from 0 to $\frac{\pi}{2}$.

$f(x)=\sin x$

Micah Hurewitz
Micah Hurewitz
Numerade Educator
01:12

Problem 76

S denotes the length of the arc of a circle of radius $r$ subtended by the central angle $\theta$. Find the missing quantity. Round answers to three decimal places.

$r=10$ miles, $s=9$ miles, $\theta=$ ?

Abhijith V
Abhijith V
Numerade Educator
00:26

Problem 76

Use a calculator to find the approximate value of each expression rounded to two decimal places.

$\sin 1^{\circ}$

Ethan Somes
Ethan Somes
Numerade Educator
01:01

Problem 76

Use the even-odd properties to find the exact value of each expression. Do not use a calculator.

$\sec \left(-\frac{\pi}{6}\right)$

Amit Srivastava
Amit Srivastava
Numerade Educator
01:53

Problem 77

Find the average rate of change of from 0 to $\frac{\pi}{2}$.

$f(x)=\cos (2 x)$

Micah Hurewitz
Micah Hurewitz
Numerade Educator
01:44

Problem 77

S denotes the length of the arc of a circle of radius $r$ subtended by the central angle $\theta$. Find the missing quantity. Round answers to three decimal places.

$r=3$ meters, $\theta=120^{\circ}, s=$ ?

Abhijith V
Abhijith V
Numerade Educator
03:24

Problem 77

A point on the terminal side of an angle $\theta$ in standard position is given. Find the exact value of each of the six trigonometric functions of $\theta$.

$(-3,4)$

Urjeet Deshmukh
Urjeet Deshmukh
Numerade Educator
00:56

Problem 77

Use properties of the trigonometric functions to find the exact value of each expression. Do not use a calculator.

$\sec ^2 18^{\circ}-\tan ^2 18^{\circ}$

Amit Srivastava
Amit Srivastava
Numerade Educator
02:27

Problem 78

Find the average rate of change of from 0 to $\frac{\pi}{2}$.

$f(x)=\sin \frac{x}{2}$

Micah Hurewitz
Micah Hurewitz
Numerade Educator
01:45

Problem 78

S denotes the length of the arc of a circle of radius $r$ subtended by the central angle $\theta$. Find the missing quantity. Round answers to three decimal places.

$r=2$ inches, $\theta=30^{\circ}, s=$ ?

Abhijith V
Abhijith V
Numerade Educator
03:11

Problem 78

A point on the terminal side of an angle $\theta$ in standard position is given. Find the exact value of each of the six trigonometric functions of $\theta$.

$(5,-12)$

Urjeet Deshmukh
Urjeet Deshmukh
Numerade Educator
00:42

Problem 78

Use properties of the trigonometric functions to find the exact value of each expression. Do not use a calculator.

$\sin ^2 40^{\circ}+\cos ^2 40^{\circ}$

Amit Srivastava
Amit Srivastava
Numerade Educator
02:49

Problem 79

Find $(f \circ g)(x)$ and $(g \circ f)(x)$, and graph each of these functions.

$f(x)=\cos x$
$g(x)=\frac{1}{2} x$

Micah Hurewitz
Micah Hurewitz
Numerade Educator
01:02

Problem 79

A denotes the area of the sector of a circle of radius $r$ formed by the central angle $\theta$. Find the missing quantity. Round answers to three decimal places.

$r=10$ meters, $\theta=\frac{1}{2}$ radian, $A=$ ?

Julie Silva
Julie Silva
Numerade Educator
03:11

Problem 79

A point on the terminal side of an angle $\theta$ in standard position is given. Find the exact value of each of the six trigonometric functions of $\theta$.

$(-1,-2)$

Urjeet Deshmukh
Urjeet Deshmukh
Numerade Educator
00:41

Problem 79

Use properties of the trigonometric functions to find the exact value of each expression. Do not use a calculator.

$\sin 80^{\circ} \csc 80^{\circ}$

Amit Srivastava
Amit Srivastava
Numerade Educator
03:24

Problem 80

Find $(f \circ g)(x)$ and $(g \circ f)(x)$, and graph each of these functions.

$f(x)=\sin x$
$g(x)=4 x$

Micah Hurewitz
Micah Hurewitz
Numerade Educator
01:02

Problem 80

A denotes the area of the sector of a circle of radius $r$ formed by the central angle $\theta$. Find the missing quantity. Round answers to three decimal places.

$r=6$ feet, $\theta=2$ radians, $A=$ ?

Julie Silva
Julie Silva
Numerade Educator
03:25

Problem 80

A point on the terminal side of an angle $\theta$ in standard position is given. Find the exact value of each of the six trigonometric functions of $\theta$.

$(2,-3)$

Urjeet Deshmukh
Urjeet Deshmukh
Numerade Educator
00:49

Problem 80

Use properties of the trigonometric functions to find the exact value of each expression. Do not use a calculator.

$\tan 10^{\circ} \cot 10^{\circ}$

Amit Srivastava
Amit Srivastava
Numerade Educator
03:04

Problem 81

Find $(f \circ g)(x)$ and $(g \circ f)(x)$, and graph each of these functions.

$f(x)=-3 x$
$g(x)=\sin x$

Micah Hurewitz
Micah Hurewitz
Numerade Educator
View

Problem 81

A denotes the area of the sector of a circle of radius $r$ formed by the central angle $\theta$. Find the missing quantity. Round answers to three decimal places.

$\theta=\frac{1}{4}$ radian, $A=6$ square centimeters, $r=$ ?

Abhijith V
Abhijith V
Numerade Educator
02:25

Problem 81

A point on the terminal side of an angle $\theta$ in standard position is given. Find the exact value of each of the six trigonometric functions of $\theta$.

$(-1,1)$

James Kiss
James Kiss
Numerade Educator
00:49

Problem 81

Use properties of the trigonometric functions to find the exact value of each expression. Do not use a calculator.

$\cot 20^{\circ}-\frac{\cos 20^{\circ}}{\sin 20^{\circ}}$

Amit Srivastava
Amit Srivastava
Numerade Educator
03:04

Problem 82

Find $(f \circ g)(x)$ and $(g \circ f)(x)$, and graph each of these functions.

$f(x)=-2 x$
$g(x)=\cos x$

Micah Hurewitz
Micah Hurewitz
Numerade Educator
View

Problem 82

A denotes the area of the sector of a circle of radius $r$ formed by the central angle $\theta$. Find the missing quantity. Round answers to three decimal places.

$\theta=\frac{1}{3}$ radian, $A=2$ square feet, $r=$ ?

Abhijith V
Abhijith V
Numerade Educator
03:17

Problem 82

A point on the terminal side of an angle $\theta$ in standard position is given. Find the exact value of each of the six trigonometric functions of $\theta$.

$(-2,-2)$

Urjeet Deshmukh
Urjeet Deshmukh
Numerade Educator
00:46

Problem 82

Use properties of the trigonometric functions to find the exact value of each expression. Do not use a calculator.

$\tan 40^{\circ}-\frac{\sin 40^{\circ}}{\cos 40^{\circ}}$

Amit Srivastava
Amit Srivastava
Numerade Educator
03:07

Problem 83

Graph $f(x)= \begin{cases}\sin x & \text { if } 0 \leq x<\frac{5 \pi}{4} \\ \cos x & \text { if } \frac{5 \pi}{4} \leq x \leq 2 \pi\end{cases}$

Natalie Anderson
Natalie Anderson
Numerade Educator
01:21

Problem 83

A denotes the area of the sector of a circle of radius $r$ formed by the central angle $\theta$. Find the missing quantity. Round answers to three decimal places.

$r=6$ meters, $A=8$ square meters, $\theta=$ ?

Abhijith V
Abhijith V
Numerade Educator
02:12

Problem 83

A point on the terminal side of an angle $\theta$ in standard position is given. Find the exact value of each of the six trigonometric functions of $\theta$.

$(0.3,0.4)$

James Kiss
James Kiss
Numerade Educator
01:15

Problem 83

Use properties of the trigonometric functions to find the exact value of each expression. Do not use a calculator.

$\tan 200^{\circ} \cdot \cot 20^{\circ}$

Amit Srivastava
Amit Srivastava
Numerade Educator
02:41

Problem 84

Graph $g(x)= \begin{cases}2 \sin x & \text { if } \quad 0 \leq x \leq \pi \\ \cos x+1 & \text { if } \quad \pi<x \leq 2 \pi\end{cases}$

Natalie Anderson
Natalie Anderson
Numerade Educator
01:24

Problem 84

A denotes the area of the sector of a circle of radius $r$ formed by the central angle $\theta$. Find the missing quantity. Round answers to three decimal places.

$r=5$ miles, $A=3$ square miles, $\theta=$ ?

Abhijith V
Abhijith V
Numerade Educator
03:47

Problem 84

A point on the terminal side of an angle $\theta$ in standard position is given. Find the exact value of each of the six trigonometric functions of $\theta$.

$\left(\frac{1}{3}, \frac{1}{4}\right)$

James Kiss
James Kiss
Numerade Educator
01:02

Problem 84

Use properties of the trigonometric functions to find the exact value of each expression. Do not use a calculator.

$\cos 400^{\circ} \cdot \sec 40^{\circ}$

Amit Srivastava
Amit Srivastava
Numerade Educator
02:24

Problem 85

Graph $y=|\sin x|,-2 \pi \leq x \leq 2 \pi$.

Micah Hurewitz
Micah Hurewitz
Numerade Educator
01:48

Problem 85

A denotes the area of the sector of a circle of radius $r$ formed by the central angle $\theta$. Find the missing quantity. Round answers to three decimal places.

$r=3$ meters, $\theta=120^{\circ}, A=$ ?

Abhijith V
Abhijith V
Numerade Educator
02:07

Problem 85

Find the exact value of:
$$
\tan 60^{\circ}+\tan 150^{\circ}
$$

James Kiss
James Kiss
Numerade Educator
01:43

Problem 85

Use properties of the trigonometric functions to find the exact value of each expression. Do not use a calculator.

$\sec \left(-\frac{\pi}{18}\right) \cdot \cos \frac{37 \pi}{18}$

Amit Srivastava
Amit Srivastava
Numerade Educator
02:24

Problem 86

Graph $y=|\cos x|,-2 \pi \leq x \leq 2 \pi$.

Micah Hurewitz
Micah Hurewitz
Numerade Educator
01:51

Problem 86

A denotes the area of the sector of a circle of radius $r$ formed by the central angle $\theta$. Find the missing quantity. Round answers to three decimal places.

$r=2$ inches, $\theta=30^{\circ}, A=$ ?

Abhijith V
Abhijith V
Numerade Educator
01:04

Problem 86

Find the exact value of:
$$
\sin 45^{\circ}+\sin 135^{\circ}+\sin 225^{\circ}+\sin 315^{\circ}
$$

James Kiss
James Kiss
Numerade Educator
01:44

Problem 86

Use properties of the trigonometric functions to find the exact value of each expression. Do not use a calculator.

$\sin \left(-\frac{\pi}{12}\right) \csc \frac{25 \pi}{12}$

Amit Srivastava
Amit Srivastava
Numerade Educator
02:51

Problem 87

The current $I$, in amperes, flowing through an ac (alternating current) circuit at time $t$, in seconds, is
$$
I(t)=120 \sin (30 \pi t) \quad t \geq 0
$$
What is the period? What is the amplitude? Graph this function over two periods.

Micah Hurewitz
Micah Hurewitz
Numerade Educator
01:17

Problem 87

Find the length s and the area A. Round answers to three decimal places.

(Graph can't copy)

Katelyn Chen
Katelyn Chen
Numerade Educator
01:51

Problem 87

Find the exact value of:
$$
\tan 40^{\circ}+\tan 140^{\circ}
$$

Urjeet Deshmukh
Urjeet Deshmukh
Numerade Educator
02:27

Problem 87

Use properties of the trigonometric functions to find the exact value of each expression. Do not use a calculator.

$\frac{\sin 70^{\circ}}{\cos \left(-430^{\circ}\right)}+\tan \left(-70^{\circ}\right)$

Amit Srivastava
Amit Srivastava
Numerade Educator
03:22

Problem 88

The current $I$, in amperes, flowing through an ac (alternating current) circuit at time $t$, in seconds, is
$$
I(t)=220 \sin (60 \pi t) \quad t \geq 0
$$
What is the period? What is the amplitude? Graph this function over two periods.

Micah Hurewitz
Micah Hurewitz
Numerade Educator
01:17

Problem 88

Find the length s and the area A. Round answers to three decimal places.

(Graph can't copy)

Katelyn Chen
Katelyn Chen
Numerade Educator
04:08

Problem 88

Find the exact value of:
$$
\sin 40^{\circ}+\sin 130^{\circ}+\sin 220^{\circ}+\sin 310^{\circ}
$$

Urjeet Deshmukh
Urjeet Deshmukh
Numerade Educator
02:11

Problem 88

Use properties of the trigonometric functions to find the exact value of each expression. Do not use a calculator.

$\frac{\sin \left(-20^{\circ}\right)}{\cos 380^{\circ}}+\tan 200^{\circ}$

Amit Srivastava
Amit Srivastava
Numerade Educator
09:06

Problem 89

The voltage $V$ produced by an ac generator is sinusoidal. As a function of time, the voltage $V$ is
$$
V(t)=V_0 \sin (2 \pi f t)
$$
where $f$ is the frequency, the number of complete oscillations (cycles) per second. [In the United States and Canada, $f$ is 60 hertz $(\mathrm{Hz})$.) The power $P$ delivered to a resistance $R$ at any time $t$ is defined as
$$
P(t)=\frac{[V(t)]^2}{R}
$$
(a) Show that $P(t)=\frac{V_0^2}{R} \sin ^2(2 \pi f t)$.
(b) The graph of $P$ is shown in the figure. Express $P$ as a sinusoidal function.
(c) Deduce that
$$
\sin ^2(2 \pi f t)=\frac{1}{2}[1-\cos (4 \pi f t)]
$$

Micah Hurewitz
Micah Hurewitz
Numerade Educator
01:17

Problem 89

Find the length s and the area A. Round answers to three decimal places.

(Graph can't copy)

Katelyn Chen
Katelyn Chen
Numerade Educator
00:46

Problem 89

If $f(\theta)=\cos \theta=0.3$, find $f(\theta+\pi)$.

James Kiss
James Kiss
Numerade Educator
01:20

Problem 89

If $\cos \theta=0.2$, find the value of:
$$
\cos \theta+\cos (\theta+2 \pi)+\cos (\theta+4 \pi)
$$

Stephanie Gaston
Stephanie Gaston
Numerade Educator
04:51

Problem 90

A one-lane highway runs through a tunnel in the shape of one-half a sine curve cycle. The opening is 44 -foot wide at road level and is 18 -foot tall at its highest point.

(a) Find an equation for the sine curve that fits the opening. Place the origin at the left end of the opening.
(b) If the road is 22 -foot wide with 11-foot shoulders on each side, what is the height of the tunnel at the edge of the road?

Micah Hurewitz
Micah Hurewitz
Numerade Educator
01:17

Problem 90

Find the length s and the area A. Round answers to three decimal places.

(Graph can't copy)

Katelyn Chen
Katelyn Chen
Numerade Educator
00:22

Problem 90

If $f(\theta)=\sin \theta=0.1$, find $f(\theta+\pi)$.

James Kiss
James Kiss
Numerade Educator
01:16

Problem 90

If $\sin \theta=0.3$, find the value of:
$$
\sin \theta+\sin (\theta+2 \pi)+\sin (\theta+4 \pi)
$$

Stephanie Gaston
Stephanie Gaston
Numerade Educator
04:31

Problem 91

Several research papers use a sinusoidal graph to model blood pressure. Suppose an individual's blood pressure is modeled by the function
$$
P(t)=20 \sin \left(\frac{7 \pi t}{3}\right)+100
$$
where the maximum value of $P$ is the systolic pressure, which is the pressure when the heart contracts (beats), the minimum value is the diastolic pressure, and $t$ is time, in seconds. The heart rate is the number of beats per minute.
(a) What is the individual's systolic pressure?
(b) What is the individual's diastolic pressure?
(c) What is the individual's heart rate?

Natalie Anderson
Natalie Anderson
Numerade Educator
01:35

Problem 91

The minute hand of a clock is 4 inches long. How far does the tip of the minute hand move in 20 minutes?
(Figure can't copy)

Uma Kumari
Uma Kumari
Numerade Educator
01:17

Problem 91

If $f(\theta)=\cot \theta=-2$, find $f(\theta+\pi)$.

James Kiss
James Kiss
Numerade Educator
01:19

Problem 91

If $\cot \theta=-2$, find the value of:
$$
\cot \theta+\cot (\theta-\pi)+\cot (\theta-2 \pi)
$$

Stephanie Gaston
Stephanie Gaston
Numerade Educator
03:58

Problem 92

The function below models the water height $H$, in feet, at a monitoring station in Charleston, South Carolina.
$$
H(t)=2.91 \sin \left(\frac{24 \pi}{149} t+1.360\right)+2.97
$$
where $t$ is the number of hours after midnight.
(a) What is the height of the water at high tide?
(b) What is the height of the water at low tide?
(c) What is the time between high and low tide?

Raushan Kumar
Raushan Kumar
Numerade Educator
01:26

Problem 92

A pendulum swings through an angle of $20^{\circ}$ each second. If the pendulum is 40 inches long, how far does its tip move each second? Round answers to two decimal places.

Julie Silva
Julie Silva
Numerade Educator
01:39

Problem 92

If $f(\theta)=\tan \theta=3$, find $f(\theta+\pi)$.

Urjeet Deshmukh
Urjeet Deshmukh
Numerade Educator
01:09

Problem 92

If $\tan \theta=3$, find the value of:
$$
\tan \theta+\tan (\theta+\pi)+\tan (\theta+2 \pi)
$$

Stephanie Gaston
Stephanie Gaston
Numerade Educator
03:44

Problem 93

The function below models the average monthly temperature $T$, in ${ }^{\circ} \mathrm{F}$, for Indianapolis, Indiana.
$$
T(x)=23.65 \sin \left(\frac{\pi}{6} x-\frac{2 \pi}{3}\right)+51.75
$$
where $x$ is the month (January $=1$, February $=2$, etc.).
(a) What is the highest average monthly temperature?
(b) What is the lowest average monthly temperature?
(c) What is the time between the highest and lowest average temperatures?

Raushan Kumar
Raushan Kumar
Numerade Educator
00:58

Problem 93

Find the area of the sector of a circle of radius 3 centimeters formed by an angle of $60^{\circ}$. Round the answer to two decimal places.

Katelyn Chen
Katelyn Chen
Numerade Educator
00:19

Problem 93

If $\cos \theta=\frac{2}{3}$, find $\sec \theta$.

James Kiss
James Kiss
Numerade Educator
03:31

Problem 93

Find the exact value of:
$$
\cos 1^{\circ}+\cos 2^{\circ}+\cos 3^{\circ}+\cdots+\cos 358^{\circ}+\cos 359^{\circ}
$$

Urjeet Deshmukh
Urjeet Deshmukh
Numerade Educator
01:59

Problem 94

The function below models the number of hours of daylight in Miami, Florida.
$$
D(x)=1.615 \sin \left(\frac{2 \pi}{365} x-1.39\right)+12.135
$$
where $x$ is the day of the year.
(a) How many hours of daylight are there on the longest day?
(b) How many hours of daylight are there on the shortest day?
(c) What is the time between the longest and shortest days?

Natalie Anderson
Natalie Anderson
Numerade Educator
06:24

Problem 94

The function
$$
h(t)=-100 \cos \left(\frac{\pi t}{50}\right)+105
$$
represents the height $h$, in feet, of a seat on a Ferris wheel as a function of time $t$, where $t$ is measured in seconds.
(a) How high does a seat on the Ferris wheel go?
(b) How close to the ground does a seat get?
(c) If a ride lasts for 5 minutes, how many times will a passenger go around?
(d) What is the linear speed of the Ferris wheel in miles per hour? Round to one decimal place.

Natalie Anderson
Natalie Anderson
Numerade Educator
01:26

Problem 94

Find the area of the sector of a circle of radius 5 meters formed by an angle of $90^{\circ}$.

Uma Kumari
Uma Kumari
Numerade Educator
00:19

Problem 94

If $\sin \theta=\frac{1}{5}$, find $\csc \theta$.

James Kiss
James Kiss
Numerade Educator
02:18

Problem 94

Find the exact value of:
$$
\sin 1^{\circ}+\sin 2^{\circ}+\sin 3^{\circ}+\cdots+\sin 358^{\circ}+\sin 359^{\circ}
$$

Urjeet Deshmukh
Urjeet Deshmukh
Numerade Educator
06:24

Problem 95

The function
$$
h(t)=-100 \cos \left(\frac{\pi t}{50}\right)+105
$$
represents the height $h$, in feet, of a seat on a Ferris wheel as a function of time $t$, where $t$ is measured in seconds.
(a) How high does a seat on the Ferris wheel go?
(b) How close to the ground does a seat get?
(c) If a ride lasts for 5 minutes, how many times will a passenger go around?
(d) What is the linear speed of the Ferris wheel in miles per hour? Round to one decimal place.

Natalie Anderson
Natalie Anderson
Numerade Educator
02:14

Problem 95

A water sprinkler sprays water over a distance of 36 feet while rotating through an angle of $150^{\circ}$. What area of lawn receives water?
(Figure can't copy)

Julie Silva
Julie Silva
Numerade Educator
00:26

Problem 95

$f(\theta)=\sin \theta$ and $g(\theta)=\cos \theta$. Find the exact value of each function below if $\theta=60^{\circ}$. Do not use a calculator.

$g(\theta)$

James Kiss
James Kiss
Numerade Educator
00:35

Problem 95

What is the domain of the cosine function?

Stephanie Gaston
Stephanie Gaston
Numerade Educator
01:59

Problem 96

The function
$$
d(t)=50 \cos \left(\frac{\pi t}{39}\right)+60
$$
represents the distance $d$, in miles, from the airport after $t$ minutes of an airplane asked to fly in a circular holding pattern.
(a) What is the plane's average distance from the airport over one cycle?
(b) How long does it take the plane to complete one cycle in the holding pattern?
(c) What is the plane's speed, in miles per hour, while in the holding pattern?
(d) If the plane travels 1.8 miles per gallon of fuel, how much fuel is used in one cycle of the holding pattern?

Nick Johnson
Nick Johnson
Numerade Educator
01:15

Problem 96

An engineer is asked to design a water sprinkler that will cover a field of 100 square yards that is in the shape of a sector of a circle of radius 15 yards. Through what angle should the sprinkler rotate?

Katelyn Chen
Katelyn Chen
Numerade Educator
00:31

Problem 96

$f(\theta)=\sin \theta$ and $g(\theta)=\cos \theta$. Find the exact value of each function below if $\theta=60^{\circ}$. Do not use a calculator.

$f(\theta)$

James Kiss
James Kiss
Numerade Educator
00:55

Problem 96

What is the domain of the sine function?

Stephanie Gaston
Stephanie Gaston
Numerade Educator
10:03

Problem 97

In the theory of biorhythms, a sine function of the form
$$
P(t)=50 \sin (\omega t)+50
$$
is used to measure the percent $P$ of a person's potential at time $t$, where $t$ is measured in days and $t=0$ is the day the person is born. Three characteristics are commonly measured: Physical potential: period of 23 days
Emotional potential: period of 28 days
Intellectual potential: period of 33 days
(a) Find $\omega$ for each characteristic.
(b) Using a graphing utility, graph all three functions on the same screen.
(c) Is there a time $t$ when all three characteristics have $100 \%$ potential? When is it?
(d) Suppose that you are 20 years old today ( $t=7305$ days). Describe your physical, emotional, and intellectual potential for the next 30 days.

Micah Hurewitz
Micah Hurewitz
Numerade Educator
02:23

Problem 97

The arm and blade of a windshield wiper have a total length of 30 inches. If the blade is 24 inches long and the wiper sweeps out an angle of $125^{\circ}$, how much window area can the blade clean?

Katelyn Chen
Katelyn Chen
Numerade Educator
00:25

Problem 97

$f(\theta)=\sin \theta$ and $g(\theta)=\cos \theta$. Find the exact value of each function below if $\theta=60^{\circ}$. Do not use a calculator.

$g\left(\frac{\theta}{2}\right)$

James Kiss
James Kiss
Numerade Educator
01:16

Problem 97

For what numbers $\theta$ is $f(\theta)=\tan \theta$ not defined?

Suman Saurav Thakur
Suman Saurav Thakur
Numerade Educator
02:54

Problem 98

If $y=A \sin (B x-C)+D, A \neq 0$, for what values of $D$ will the graph lie completely below the $x$-axis?

Natalie Anderson
Natalie Anderson
Numerade Educator
04:40

Problem 98

The windshield of a car has a total length of arm and blade of 9 inches, and rotates back and forth through an angle of $84^{\circ}$. What is the area of the portion of the windshield cleaned by the 7-in wiper blade?

Jessica Horn
Jessica Horn
Numerade Educator
00:35

Problem 98

$f(\theta)=\sin \theta$ and $g(\theta)=\cos \theta$. Find the exact value of each function below if $\theta=60^{\circ}$. Do not use a calculator.

$f\left(\frac{\theta}{2}\right)$

James Kiss
James Kiss
Numerade Educator
02:02

Problem 98

For what numbers $\theta$ is $f(\theta)=\cot \theta$ not defined?

Stephanie Gaston
Stephanie Gaston
Numerade Educator
02:36

Problem 99

If $A \neq 0$, find the intercepts of the graph of
$$
y=A \cos [B(x-C)]+A
$$

Natalie Anderson
Natalie Anderson
Numerade Educator
02:25

Problem 99

An object is traveling around a circle with a radius of 12 centimeters. If in 40 seconds a central angle of $\frac{1}{6}$ radian is swept out, what are the linear and angular speeds of the object?

Julie Silva
Julie Silva
Numerade Educator
00:25

Problem 99

$f(\theta)=\sin \theta$ and $g(\theta)=\cos \theta$. Find the exact value of each function below if $\theta=60^{\circ}$. Do not use a calculator.

$[g(\theta)]^2$

James Kiss
James Kiss
Numerade Educator
01:52

Problem 99

For what numbers $\theta$ is $f(\theta)=\csc \theta$ not defined?

Stephanie Gaston
Stephanie Gaston
Numerade Educator
01:39

Problem 100

Explain how you would scale the $x$-axis and $y$-axis before graphing $y=3 \cos (\pi x)$.

Micah Hurewitz
Micah Hurewitz
Numerade Educator
01:29

Problem 100

A neighborhood carnival has a Ferris wheel with a radius of 30 feet. You measure the time it takes for one revolution to be 70 seconds. What is the linear speed (in feet per second) of this Ferris wheel? What is the angular speed in radians per second?

Katelyn Chen
Katelyn Chen
Numerade Educator
00:30

Problem 100

$f(\theta)=\sin \theta$ and $g(\theta)=\cos \theta$. Find the exact value of each function below if $\theta=60^{\circ}$. Do not use a calculator.

$[f(\theta)]^2$

James Kiss
James Kiss
Numerade Educator
01:38

Problem 100

For what numbers $\theta$ is $f(\theta)=\sec \theta$ not defined?

Stephanie Gaston
Stephanie Gaston
Numerade Educator
01:40

Problem 101

Explain the term amplitude as it relates to the graph of a sinusoidal function.

Micah Hurewitz
Micah Hurewitz
Numerade Educator
01:45

Problem 101

A centrifugal force ride, similar to the Gravitron, spins at a rate of 22 revolutions per minute. If the diameter of the ride is 13 meters, what is the linear speed of the passengers in kilometers per hour?

Dharmendra Jain
Dharmendra Jain
Numerade Educator
00:25

Problem 101

$f(\theta)=\sin \theta$ and $g(\theta)=\cos \theta$. Find the exact value of each function below if $\theta=60^{\circ}$. Do not use a calculator.

$g(2 \theta)$

James Kiss
James Kiss
Numerade Educator
01:06

Problem 101

What is the range of the cosine function?

Stephanie Gaston
Stephanie Gaston
Numerade Educator
01:38

Problem 102

Explain the term period as it relates to the graph of a sinusoidal function.

Micah Hurewitz
Micah Hurewitz
Numerade Educator
01:57

Problem 102

A gondola on an amusement park ride spins at a speed of 11 revolutions per minute. If the gondola is 23 feet from the ride's center, what is the linear speed of the gondola in miles per hour?

Dharmendra Jain
Dharmendra Jain
Numerade Educator
00:27

Problem 102

$f(\theta)=\sin \theta$ and $g(\theta)=\cos \theta$. Find the exact value of each function below if $\theta=60^{\circ}$. Do not use a calculator.

$f(2 \theta)$

James Kiss
James Kiss
Numerade Educator
00:49

Problem 102

What is the range of the sine function?

Stephanie Gaston
Stephanie Gaston
Numerade Educator
01:40

Problem 103

Explain how the amplitude and period of a sinusoidal graph are used to establish the scale on each coordinate axis.

Micah Hurewitz
Micah Hurewitz
Numerade Educator
02:57

Problem 103

As of January 2018, the world's tallest wind turbine was located in Gaildorf, Germany, with a hub height of 178 meters and a rotor diameter of 137 meters. If the blades turn at a rate of 14 revolutions per minute, what is the linear speed of the blade tip, in $\mathrm{km} / \mathrm{h}$ ?

PR
Paul Ridder
Numerade Educator
00:25

Problem 103

$f(\theta)=\sin \theta$ and $g(\theta)=\cos \theta$. Find the exact value of each function below if $\theta=60^{\circ}$. Do not use a calculator.

$2 g(\theta)$

James Kiss
James Kiss
Numerade Educator
01:04

Problem 103

What is the range of the cotangent function?

Stephanie Gaston
Stephanie Gaston
Numerade Educator
02:32

Problem 104

Find an application in your major field that leads to a sinusoidal graph. Write a summary of your findings.

Anjali Kurse
Anjali Kurse
Numerade Educator
01:12

Problem 104

A drive has a maximum speed of 10,000 revolutions per minute. If a disc has a diameter of $14 \mathrm{~cm}$, what is the linear speed, in $\mathrm{km} / \mathrm{h}$, of a point $6 \mathrm{~cm}$ from the center if the disc is spinning at a rate of 8000 revolutions per minute?

Narayan Hari
Narayan Hari
Numerade Educator
00:35

Problem 104

$f(\theta)=\sin \theta$ and $g(\theta)=\cos \theta$. Find the exact value of each function below if $\theta=60^{\circ}$. Do not use a calculator.

$2 f(\theta)$

James Kiss
James Kiss
Numerade Educator
01:33

Problem 104

What is the range of the tangent function?

Stephanie Gaston
Stephanie Gaston
Numerade Educator
02:39

Problem 105

The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

If $f(x)=x^2-5 x+1$, find $\frac{f(x+h)-f(x)}{h}$.

Suman Saurav Thakur
Suman Saurav Thakur
Numerade Educator
03:41

Problem 105

The diameter of each wheel of a bicycle is 26 inches. If you are traveling at a speed of 40 miles per hour on this bicycle, through how many revolutions per minute are the wheels turning?

PR
Paul Ridder
Numerade Educator
00:25

Problem 105

$f(\theta)=\sin \theta$ and $g(\theta)=\cos \theta$. Find the exact value of each function below if $\theta=60^{\circ}$. Do not use a calculator.

$g(-\theta)$

James Kiss
James Kiss
Numerade Educator
02:27

Problem 105

What is the range of the cosecant function?

Stephanie Gaston
Stephanie Gaston
Numerade Educator
02:20

Problem 106

The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

Find the vertex of the graph of $g(x)=-3 x^2+12 x-7$.

Raushan Kumar
Raushan Kumar
Numerade Educator
02:09

Problem 106

The radius of each wheel of a car is 15 inches. If the wheels are turning at the rate of 3 revolutions per second, how fast is the car moving? Express your answer in inches per second and in miles per hour.

Katelyn Chen
Katelyn Chen
Numerade Educator
00:37

Problem 106

$f(\theta)=\sin \theta$ and $g(\theta)=\cos \theta$. Find the exact value of each function below if $\theta=60^{\circ}$. Do not use a calculator.

$f(-\theta)$

James Kiss
James Kiss
Numerade Educator
03:04

Problem 106

What is the range of the secant function?

Stephanie Gaston
Stephanie Gaston
Numerade Educator
04:42

Problem 107

The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

Find the intercepts of the graph of $h(x)=3|x+2|-1$.

Anjali Kurse
Anjali Kurse
Numerade Educator
02:07

Problem 107

If the viewing angle for a $600 \mathrm{~mm}$ lens is $4^{\circ} 6^{\prime}$, use arc length to approximate the field width of the lens at a distance of 860 feet.

Caitlin Hunter
Caitlin Hunter
Numerade Educator
01:17

Problem 107

$f(x)=\sin x, g(x)=\cos x, h(x)=2 x$, and $p(x)=\frac{x}{2}$. Find the value of each of the following:

$(f-g)\left(60^{\circ}\right)$

Ethan Somes
Ethan Somes
Numerade Educator
01:24

Problem 107

Is the cosine function even, odd, or neither? Is its graph symmetric? With respect to what?

Stephanie Gaston
Stephanie Gaston
Numerade Educator
01:17

Problem 108

The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

Solve: $3 x-2(5 x+16)=-3 x+4(8+x)$

Allison Knapp
Allison Knapp
Numerade Educator
01:35

Problem 108

If the viewing angle for an $800 \mathrm{~mm}$ lens is $1^{\circ} 42^{\prime}$, use arc length to approximate the field width of the lens at a distance of 920 feet.

Caitlin Hunter
Caitlin Hunter
Numerade Educator
01:27

Problem 108

$f(x)=\sin x, g(x)=\cos x, h(x)=2 x$, and $p(x)=\frac{x}{2}$. Find the value of each of the following:

$(f+g)\left(30^{\circ}\right)$

Ethan Somes
Ethan Somes
Numerade Educator
01:48

Problem 108

Is the sine function even, odd, or neither? Is its graph symmetric? With respect to what?

Stephanie Gaston
Stephanie Gaston
Numerade Educator
01:38

Problem 109

The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

Determine the time required for an investment of $$\$ 1500$$ to double if it earns $4 \%$ interest compounded quarterly. Round your answer to one decimal place.

Sheryl Ezze
Sheryl Ezze
Numerade Educator
01:39

Problem 109

The latitude of a location $L$ is the angle formed by a ray drawn from the center of Earth to the equator and a ray drawn from the center of Earth to $L$. See the figure.
(Figure can't copy)

Earth rotates on an axis through its poles. The distance from the axis to a location on Earth at $40^{\circ}$ north latitude is about 3033.5 miles. Therefore, a location on Earth at $40^{\circ}$ north latitude is spinning on a circle of radius 3033.5 miles. Compute the linear speed on the surface of Earth at $40^{\circ}$ north latitude.

Dharmendra Jain
Dharmendra Jain
Numerade Educator
01:03

Problem 109

$f(x)=\sin x, g(x)=\cos x, h(x)=2 x$, and $p(x)=\frac{x}{2}$. Find the value of each of the following:

$(f \cdot g)\left(\frac{4 \pi}{3}\right)$

James Kiss
James Kiss
Numerade Educator
01:41

Problem 109

Is the cotangent function even, odd, or neither? Is its graph symmetric? With respect to what?

Stephanie Gaston
Stephanie Gaston
Numerade Educator
00:59

Problem 110

The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

Solve $e^{3 x}=7$.

Raushan Kumar
Raushan Kumar
Numerade Educator
01:32

Problem 110

The latitude of a location $L$ is the angle formed by a ray drawn from the center of Earth to the equator and a ray drawn from the center of Earth to $L$. See the figure.
(Figure can't copy)

A planet rotates on an axis through its poles and 1 revolution takes 1 day ( 1 day is 18 hours). The distance from the axis to a location on the planet $30^{\circ}$ north latitude is about 2166.5 miles. Therefore, a location on the planet at $30^{\circ}$ north latitude is spinning on a circle of radius 2166.5 miles. Compute the linear speed on the surface of the planet at $30^{\circ}$ north latitude.

Dharmendra Jain
Dharmendra Jain
Numerade Educator
01:08

Problem 110

$f(x)=\sin x, g(x)=\cos x, h(x)=2 x$, and $p(x)=\frac{x}{2}$. Find the value of each of the following:

$(f \cdot g)\left(\frac{3 \pi}{4}\right)$

James Kiss
James Kiss
Numerade Educator
01:26

Problem 110

Is the tangent function even, odd, or neither? Is its graph symmetric? With respect to what?

Stephanie Gaston
Stephanie Gaston
Numerade Educator
02:05

Problem 111

The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

Find the oblique asymptote of $g(x)=\frac{4 x^3+6 x^2-3 x+1}{2 x^2-4 x+3}$.

Natalie Anderson
Natalie Anderson
Numerade Educator
02:40

Problem 111

The mean distance of a moon from a planet is $2.5 \times 10^5$ miles. Assuming that the orbit of the moon around the planet is circular and that 1 revolution takes 24.3 days ( 1 day is 26 hours), find the linear speed of the moon. Express your answer in miles per hour.

Yujie Wang
Yujie Wang
College of San Mateo
01:11

Problem 111

$f(x)=\sin x, g(x)=\cos x, h(x)=2 x$, and $p(x)=\frac{x}{2}$. Find the value of each of the following:

$\left(g^{\circ} p\right)\left(60^{\circ}\right)$

Ethan Somes
Ethan Somes
Numerade Educator
01:13

Problem 111

Is the cosecant function even, odd, or neither? Is its graph symmetric? With respect to what?

Stephanie Gaston
Stephanie Gaston
Numerade Educator
03:34

Problem 112

The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

Determine the interval on which $f(x)=-6 x^2-19 x+7$ is decreasing.

Raushan Kumar
Raushan Kumar
Numerade Educator
01:11

Problem 112

The mean distance of Earth from the Sun is $9.29 \times 10^7$ miles. Assuming that the orbit of Earth around the Sun is circular and that 1 revolution takes 365 days, find the linear speed of Earth. Express your answer in miles per hour.

Katelyn Chen
Katelyn Chen
Numerade Educator
01:48

Problem 112

$f(x)=\sin x, g(x)=\cos x, h(x)=2 x$, and $p(x)=\frac{x}{2}$. Find the value of each of the following:

$(f \circ h)\left(\frac{\pi}{6}\right)$

Ethan Somes
Ethan Somes
Numerade Educator
01:26

Problem 112

Is the secant function even, odd, or neither? Is its graph symmetric? With respect to what?

Stephanie Gaston
Stephanie Gaston
Numerade Educator
00:59

Problem 113

The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

Write the set $\left\{x \mid x \leq-2\right.$ or $\left.x>\frac{4}{3}\right\}$ using interval notation.

Raushan Kumar
Raushan Kumar
Numerade Educator
01:31

Problem 113

Two pulleys, one with radius 2 inches and the other with radius 8 inches, are connected by a belt. (See the figure.) If the 2 -inch pulley is caused to rotate at 3 revolutions per minute, determine the revolutions per minute of the 8-inch pulley.

Katelyn Chen
Katelyn Chen
Numerade Educator
00:48

Problem 113

$f(x)=\sin x, g(x)=\cos x, h(x)=2 x$, and $p(x)=\frac{x}{2}$. Find the value of each of the following:

$(h \circ f)\left(\frac{5 \pi}{6}\right)$

James Kiss
James Kiss
Numerade Educator
02:36

Problem 113

Use the periodic and even-odd properties.

If $f(\theta)=\cos \theta$ and $f(a)=\frac{1}{4}$, find the exact value of:
(a) $f(-a)$
(b) $f(a)+f(a+2 \pi)+f(a-2 \pi)$

Amit Srivastava
Amit Srivastava
Numerade Educator
04:37

Problem 114

The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

Solve: $\log (x-3)-\log (x+3)=\log (x-4)$

Raushan Kumar
Raushan Kumar
Numerade Educator
02:04

Problem 114

Two pulleys, one with radius $r_1$ and the other with radius $r_2$, are connected by a belt. The pulley with radius $r_1$ rotates at $\omega_1$ revolutions per minute, whereas the pulley with radius $r_2$ rotates at $\omega_2$ revolutions per minute. Show that
$$
\frac{r_1}{r_2}=\frac{\omega_2}{\omega_1}
$$
Use this result to rework Problem 113.

Yujie Wang
Yujie Wang
College of San Mateo
01:16

Problem 114

$f(x)=\sin x, g(x)=\cos x, h(x)=2 x$, and $p(x)=\frac{x}{2}$. Find the value of each of the following:

$(p \circ g)\left(315^{\circ}\right)$

James Kiss
James Kiss
Numerade Educator
02:29

Problem 114

Use the periodic and even-odd properties.

If $f(x)=\cos (x)$ and $f(a)=\frac{1}{2}$, find the exact value of the following.
(a) $f(-a)$
(b) $f(a)+f(a+2 \pi)+f(a+4 \pi)$

Abdul Vahid M
Abdul Vahid M
Numerade Educator
01:25

Problem 115

To approximate the speed of the current of a river, a circular paddle wheel with radius $5 \mathrm{ft}$. is lowered into the water. If the current causes the wheel to rotate at a speed of 15 revolutions per minute, what is the speed of the current?

Katelyn Chen
Katelyn Chen
Numerade Educator
01:34

Problem 115

$f(x)=\sin x, g(x)=\cos x, h(x)=2 x$, and $p(x)=\frac{x}{2}$. Find the value of each of the following:

(a) Find $g\left(\frac{\pi}{6}\right)$. What point is on the graph of $g$ ?
(b) Assuming $0 \leq x \leq \frac{\pi}{2}, g$ is one-to-one.* Use the result of part (a) to find a point on the graph of $g^{-1}$.
(c) What point is on the graph of $y=2 g\left(x-\frac{\pi}{6}\right)$ if $x=\frac{\pi}{6}$ ?

Eleanor Johnson
Eleanor Johnson
Numerade Educator
02:22

Problem 115

Use the periodic and even-odd properties.

If $f(\theta)=\cot \theta$ and $f(a)=-3$, find the exact value of:
(a) $f(-a)$
(b) $f(a)+f(a+\pi)+f(a+4 \pi)$

Amit Srivastava
Amit Srivastava
Numerade Educator
03:02

Problem 116

$\mathrm{A}$ spin balancer rotates the wheel of a car at 480 revolutions per minute. If the diameter of the wheel is 26 inches, what road speed is being tested? Express your answer in miles per hour. At how many revolutions per minute should the balancer be set to test a road speed of 80 miles per hour?

Katelyn Chen
Katelyn Chen
Numerade Educator
01:48

Problem 116

$f(x)=\sin x, g(x)=\cos x, h(x)=2 x$, and $p(x)=\frac{x}{2}$. Find the value of each of the following:

(a) Find $f\left(\frac{\pi}{4}\right)$. What point is on the graph of $f$ ?
(b) Assuming $0 \leq x \leq \frac{\pi}{2}, f$ is one-to-one.* Use the result of part (a) to find a point on the graph of $f^{-1}$.
(c) What point is on the graph of $y=f\left(x+\frac{\pi}{4}\right)-3$ if $x=\frac{\pi}{4}$ ?

Eleanor Johnson
Eleanor Johnson
Numerade Educator
02:55

Problem 116

Use the periodic and even-odd properties.

If $f(x)=\cot (x)$ and $f(a)=2$, find the exact value of the following.
(a) $f(-a)$
(b) $f(a)+f(a+\pi)+f(a+2 \pi)$

Stephanie Gaston
Stephanie Gaston
Numerade Educator
02:28

Problem 117

At a museum you can see the four cable lines that are used to pull cable cars up and down a hill. Each cable travels at a speed of 8.65 miles per hour, caused by a rotating wheel whose diameter is 9.5 feet. How fast is the wheel rotating? Express your answer in revolutions per minute.

Dharmendra Jain
Dharmendra Jain
Numerade Educator
02:35

Problem 117

Find two negative and three positive angles, expressed in radians, for which the point on the unit circle that corresponds to each angle is $\left(-\frac{1}{2}, \frac{\sqrt{3}}{2}\right)$.

James Kiss
James Kiss
Numerade Educator
02:13

Problem 117

Use the periodic and even-odd properties.

If $f(\theta)=\csc \theta$ and $f(a)=2$, find the exact value of:
(a) $f(-a)$
(b) $f(a)+f(a+2 \pi)+f(a+4 \pi)$

Amit Srivastava
Amit Srivastava
Numerade Educator
03:21

Problem 118

Naples, Florida, is about 90 miles due west of Ft. Lauderdale. How much sooner would a person in $\mathrm{Ft}$. Lauderdale first see the rising Sun than a person in Naples? See Hint, top right.

Arnelia K
Arnelia K
Numerade Educator
02:10

Problem 118

Find two negative and three positive angles, expressed in radians, for which the point on the unit circle that corresponds to each angle is $\left(-\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)$.

James Kiss
James Kiss
Numerade Educator
02:14

Problem 118

Use the periodic and even-odd properties.

If $f(x)=\sec (x)$ and $f(a)=-11$, find the exact value of the following.
(a) $f(-a)$
(b) $f(a)+f(a+\pi)+f(a+4 \pi)$

Abdul Vahid M
Abdul Vahid M
Numerade Educator
01:10

Problem 119

How fast would an object have to travel on the surface of Jupiter at the equator to keep up with the Sun (that is, so the Sun would appear to remain in the same position in the sky)? Use the facts that the radius of Jupiter is approximately 44,360 miles and its revolution is approximately 10 hours.

AG
Ankit Gupta
Numerade Educator
02:08

Problem 119

Use a calculator in radian mode to complete the following table.
What can be concluded about the value of $f(\theta)=\frac{\tan \theta}{\theta}$ as $\theta$ approaches 0 ?
$$
\begin{array}{|lllllllll|}
\hline \theta & 0.5 & 0.4 & 0.2 & 0.1 & 0.01 & 0.001 & 0.0001 & 0.00001 \\
\hline \tan \theta & & & & & & & \\
f(\theta)=\frac{\tan \theta}{\theta} & & & & & & & & \\
\hline
\end{array}
$$

Ethan Somes
Ethan Somes
Numerade Educator
06:41

Problem 119

Two oceanfront homes are located 8 miles apart on a straight stretch of beach, each a distance of 1 mile from a paved path that parallels the ocean. Sally can jog 8 miles per hour on the paved path, but only 3 miles per hour in the sand on the beach. Because a river flows directly between the two houses, it is necessary to jog in the sand to the road, continue on the path, and then jog directly back in the sand to get from one house to the other. See the figure. The time $T$ to get from one house to the other as a function of the angle $\theta$ shown in the figure is
$$
T(\theta)=1+\frac{2}{3 \sin \theta}-\frac{1}{4 \tan \theta} \quad 0<\theta<\frac{\pi}{2}
$$
(a) Calculate the time $T$ for $\tan \theta=\frac{1}{4}$.
(b) Describe the path taken.
(c) Explain why $\theta$ must be larger than $14^{\circ}$.

Amit Srivastava
Amit Srivastava
Numerade Educator
02:09

Problem 120

A nautical mile equals the length of the arc subtended by a central angle of 1 minute on a great circle on the surface of Earth. See the figure. If the radius of Earth is taken as 3960 miles, express 1 nautical mile in terms of ordinary, or statute, miles.
(Figure can't copy)

Sheryl Ezze
Sheryl Ezze
Numerade Educator
01:47

Problem 120

Use a calculator in radian mode to complete the following table.
What do you conjecture about the value of $g(\theta)=\frac{\cos \theta-1}{\theta}$ as $\theta$ approaches 0 ?
$$
\begin{array}{|lllllllll|}
\hline \theta & 0.5 & 0.4 & 0.2 & 0.1 & 0.01 & 0.001 & 0.0001 & 0.00001 \\
\hline \cos \theta-1 & & & & & & & & \\
g(\theta)=\frac{\cos \theta-1}{\theta} & & & & & & & & \\
\hline
\end{array}
$$

Eleanor Johnson
Eleanor Johnson
Numerade Educator
06:12

Problem 120

From a parking lot you want to walk to a house on the ocean. The house is located $1480 \mathrm{ft}$ down a paved path that parallels the beach, which is $740 \mathrm{ft}$ wide. Along the path, you can walk $330 \mathrm{ft} / \mathrm{min}$, but on the beach you can only walk $130 \mathrm{ft} / \mathrm{min}$. Calculate the time $T$ if you walk directly from the parking lot to the house.

AG
Ankit Gupta
Numerade Educator
01:32

Problem 121

Eratosthenes of Cyrene (276-195 BC) was a Greek scholar who lived and worked in Cyrene and Alexandria. One day while visiting in Syene, he noticed that the Sun's rays shone directly down a well. On this date 1 year later, in Alexandria, which is 500 miles due north of Syene, he measured the angle of the Sun to be about 7.2 degrees. See the figure. Use this information to approximate the radius and circumference of Earth.
(Figure can't copy)

Dharmendra Jain
Dharmendra Jain
Numerade Educator
02:10

Problem 121

Find the range $R$ and maximum height $H$. Round answers to two decimal places. See the discussion on the previous page.

The projectile is fired at an angle of $30^{\circ}$ to the horizontal with an initial speed of 150 meters per second.

Ethan Somes
Ethan Somes
Numerade Educator
04:44

Problem 121

In predator-prey relationships, the populations of the predator and prey are often cyclical. In a conservation area, rangers monitor the red fox population and have determined that the population can be modeled by the function
$$
P(t)=40 \cos \left(\frac{\pi t}{6}\right)+110
$$
where $t$ is the number of months from the time monitoring began. Use the model to estimate the population of red foxes in the conservation area after 10 months, 20 months, and 30 months.

Abdul Vahid M
Abdul Vahid M
Numerade Educator
01:54

Problem 122

For a 60-foot Little League Baseball field, the distance from home base to the nearest fence (or other obstruction) in fair territory should be a minimum of 200 feet. The commissioner of parks and recreation is making plans for a new 60 -foot field. Because of limited ground availability, he will use the minimum required distance to the outfield fence. To increase safety, however, he plans to include a 10 -foot wide warning track on the inside of the fence. To further increase safety, the fence and warning track will extend both directions into foul territory. In total, the arc formed by the outfield fence (including the extensions into the foul territories) will be subtended by a central angle at home plate measuring $96^{\circ}$, as illustrated.
(a) Determine the length of the outfield fence.
(b) Determine the area of the warning track.
(Figure can't copy)

Katelyn Chen
Katelyn Chen
Numerade Educator
02:03

Problem 122

Find the range $R$ and maximum height $H$. Round answers to two decimal places. See the discussion on the previous page.

The projectile is fired at an angle of $45^{\circ}$ to the horizontal with an initial speed of 150 feet per second.

Ethan Somes
Ethan Somes
Numerade Educator
04:30

Problem 122

Normal resting lung volume $V$, in $\mathrm{mL}$, for adult men varies over the breathing cycle and can be approximated by the model
$$
V(t)=250 \sin \left[\frac{2 \pi(t-1.25)}{5}\right]+2650
$$
where $t$ is the number of seconds after breathing begins. Use the model to estimate the volume of air in a man's lungs after 2.5 seconds, 10 seconds, and 17 seconds.

Yujie Wang
Yujie Wang
College of San Mateo
01:31

Problem 123

A dog is attached to a 35 -foot rope fastened to the outside corner of a fenced-in garden that measures 30 feet by 36 feet. Assuming that the dog cannot enter the garden, compute the exact area that the dog can wander.

Katelyn Chen
Katelyn Chen
Numerade Educator
02:04

Problem 123

Find the range $R$ and maximum height $H$. Round answers to two decimal places. See the discussion on the previous page.

The projectile is fired at an angle of $50^{\circ}$ to the horizontal with an initial speed of 200 feet per second.

Ethan Somes
Ethan Somes
Numerade Educator
04:06

Problem 123

Show that the range of the tangent function is the set of all real numbers.

Amit Srivastava
Amit Srivastava
Numerade Educator
01:34

Problem 124

See the figure. The measure of arc $\widehat{B E}$ is $2 \pi$. Find the exact area of the portion of the rectangle $A B C D$ that falls outside of the circle whose center is at $A$."
(Figure can't copy)

Kratika Bhadauria
Kratika Bhadauria
Numerade Educator
01:57

Problem 124

Find the range $R$ and maximum height $H$. Round answers to two decimal places. See the discussion on the previous page.

The projectile is fired at an angle of $25^{\circ}$ to the horizontal with an initial speed of 500 meters per second.

Ethan Somes
Ethan Somes
Numerade Educator
04:04

Problem 124

Show that the range of the cotangent function is the set of all real numbers.

Amit Srivastava
Amit Srivastava
Numerade Educator
04:54

Problem 125

A bicycle has a pedal drive wheel with radius 5.2 inches and a rear $\operatorname{cog}$ wheel with radius 1.8 inches. See the figure. How many revolutions will the pedals need to make to move the bicycle 50 feet if the wheels have a diameter of 30 inches? Round to the nearest tenth.
(Figure can't copy)

Arnelia K
Arnelia K
Numerade Educator
04:26

Problem 125

See the figure.
(Figure can't copy)
If friction is ignored, the time $t$ (in seconds) required for a block to slide down an inclined plane (see the figure) is given by the formula $t$
$$
t(\theta)=\sqrt{\frac{2 a}{g \sin \theta \cos \theta}},
$$
where $a$ is the length (in feet) of the base and $g \approx 32$ feet per second per second is the acceleration due to gravity.
How long does it take a block to slide down an inclined plane with base $a=70$ feet when
(a) $\theta=30^{\circ}$
(b) $\theta=45^{\circ}$
(c) $\theta=60^{\circ}$

James Kiss
James Kiss
Numerade Educator
04:31

Problem 125

Show that the period of $f(\theta)=\sin \theta$ is $2 \pi$.

Amit Srivastava
Amit Srivastava
Numerade Educator
00:44

Problem 126

Do you prefer to measure angles using degrees or radians? Provide justification and a rationale for your choice.

Katelyn Chen
Katelyn Chen
Numerade Educator
02:54

Problem 126

In a certain piston engine, the distance $x$ (in centimeters) from the center of the drive shaft to the head of a piston is given by the function below, where $\theta$ is the angle between the crank and the path of the piston head. See the figure. Find $x$ when $\theta=30^{\circ}$ and $\theta=45^{\circ}$.
$$
x(\theta)=\sin \theta+\sqrt{49+0.6 \sin (2 \theta)}
$$
(Figure can't copy)

James Kiss
James Kiss
Numerade Educator
03:22

Problem 126

Show that the period of $f(\theta)=\cos \theta$ is $2 \pi$.

Amit Srivastava
Amit Srivastava
Numerade Educator
01:04

Problem 127

What is 1 radian? What is 1 degree?

Katelyn Chen
Katelyn Chen
Numerade Educator
01:51

Problem 127

Two homes are located 4 miles apart, each 1 mile from a road that parallels the ocean. Sally can jog $4 \mathrm{mph}$ along the road, but only $2 \mathrm{mph}$ in the sand.
Because of a river between the two houses, it is necessary to jog on the sand to the road, continue on the road, and then jog on the sand to get from one house to the other. For $0^{\circ}<\theta<90^{\circ}$, the time $T$ to get from one house to the other is a function of $\theta$, as shown.
$$
T(\theta)=1+\frac{2}{2 \sin \theta}-\frac{1}{2 \tan \theta}, \quad 0^{\circ}<\theta<90^{\circ}
$$
(Figure can't copy)
(a) Calculate the time $T$ for $\theta=30^{\circ}$. How long is Sally on the paved road?
(b) Calculate the time $T$ for $\theta=45^{\circ}$. How long is Sally on the paved road?
(c) Calculate the time $T$ for $\theta=60^{\circ}$. How long is Sally on the paved road?
(d) Calculate the time $T$ for $\theta=90^{\circ}$. Describe the path taken. Why can't the formula for $T$ be used?

Erika Bustos
Erika Bustos
Numerade Educator
01:23

Problem 127

Show that the period of $f(\theta)=\sec \theta$ is $2 \pi$.

Amit Srivastava
Amit Srivastava
Numerade Educator
00:39

Problem 128

Which angle has the larger measure: 1 degree or 1 radian? Or are they equal?

Katelyn Chen
Katelyn Chen
Numerade Educator
03:30

Problem 128

A designer of decorative art plans to market solid gold spheres encased in clear crystal cones. Each sphere is of fixed radius $R$ and will be enclosed in a cone of height $h$ and radius $r$. See the figure. Many cones can be used to enclose the sphere, each having a different slant angle $\theta$. The volume $V$ of the cone can be expressed as a function of the slant angle $\theta$ of the cone as
$$
V(\theta)=\frac{1}{3} \pi R^3 \frac{(1+\sec \theta)^3}{(\tan \theta)^2} \quad 0^{\circ}<\theta<90^{\circ}
$$
What volume $V$ is required to enclose a sphere of radius 2 centimeters in a cone whose slant angle $\theta$ is $30^{\circ}$ ? $45^{\circ}$ ? $60^{\circ}$ ?
(Figure can't copy)

Erika Bustos
Erika Bustos
Numerade Educator
01:59

Problem 128

Show that the period of $f(\theta)=\csc \theta$ is $2 \pi$.

Amit Srivastava
Amit Srivastava
Numerade Educator
00:30

Problem 129

Explain the difference between linear speed and angular speed.

Katelyn Chen
Katelyn Chen
Numerade Educator
01:27

Problem 129

The viewing angle, $\theta$, of an object is the angle the object forms at the lens of the viewer's eye. This is also known as the perceived or angular size of the object. The viewing angle is related to the object's height, $H$, and distance from the viewer, $D$, through the formula $\tan \frac{\theta}{2}=\frac{H}{2 D}$.

While driving, Arletha observes the car in front of her with a viewing angle of $26^{\circ}$. If the car is 5.5 feet wide, how close is Arletha to the car in front of her?

Sheryl Ezze
Sheryl Ezze
Numerade Educator
03:33

Problem 129

Show that the period of $f(\theta)=\tan \theta$ is $\pi$.

Amit Srivastava
Amit Srivastava
Numerade Educator
02:19

Problem 130

For a circle of radius $r$, a central angle of $\theta$ degrees subtends an arc whose length $s$ is $s=\frac{\pi}{180} r \theta$. Discuss whether this statement is true or false. Defend your position.

Abhijith V
Abhijith V
Numerade Educator
01:27

Problem 130

The viewing angle, $\theta$, of an object is the angle the object forms at the lens of the viewer's eye. This is also known as the perceived or angular size of the object. The viewing angle is related to the object's height, $H$, and distance from the viewer, $D$, through the formula $\tan \frac{\theta}{2}=\frac{H}{2 D}$.

The Washington Monument in Washington, D.C. is 555 feet tall. If a tourist sees the monument with a viewing angle of $8^{\circ}$, how far away, to the nearest foot, is she from the monument?

Sheryl Ezze
Sheryl Ezze
Numerade Educator
01:41

Problem 130

Show that the period of $f(\theta)=\cot \theta$ is $\pi$.

Amit Srivastava
Amit Srivastava
Numerade Educator
01:10

Problem 131

Discuss why ships and airplanes use nautical miles to measure distance. Explain the difference between a nautical mile and a statute mile.

Katelyn Chen
Katelyn Chen
Numerade Educator
01:02

Problem 131

The viewing angle, $\theta$, of an object is the angle the object forms at the lens of the viewer's eye. This is also known as the perceived or angular size of the object. The viewing angle is related to the object's height, $H$, and distance from the viewer, $D$, through the formula $\tan \frac{\theta}{2}=\frac{H}{2 D}$.

A forest ranger views a tree that is 190 feet away with a viewing angle of $21^{\circ}$. How tall is the tree?

Sheryl Ezze
Sheryl Ezze
Numerade Educator
02:42

Problem 131

Prove the reciprocal identities given in identity (2).

Amit Srivastava
Amit Srivastava
Numerade Educator
00:58

Problem 132

Investigate the way that speed bicycles work. In particular, explain the differences and similarities between 5 -speed and 9-speed derailleurs. Be sure to include a discussion of linear speed and angular speed.

Katelyn Chen
Katelyn Chen
Numerade Educator
01:41

Problem 132

The viewing angle, $\theta$, of an object is the angle the object forms at the lens of the viewer's eye. This is also known as the perceived or angular size of the object. The viewing angle is related to the object's height, $H$, and distance from the viewer, $D$, through the formula $\tan \frac{\theta}{2}=\frac{H}{2 D}$.

An astronomer observes the moon with a viewing angle of $0.52^{\circ}$. If the moon's average distance from Earth is $384,400 \mathrm{~km}$, what is its radius to the nearest kilometer?

Pawan Yadav
Pawan Yadav
Numerade Educator
02:30

Problem 132

Prove the quotient identities given in identity (3).

Amit Srivastava
Amit Srivastava
Numerade Educator
01:20

Problem 133

Are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

Find the zero of $f(x)=3 x+7$.

Dharmendra Jain
Dharmendra Jain
Numerade Educator
15:06

Problem 133

An object is fired at an angle $\theta$ to the horizontal with an initial speed of $v_0$ feet per second. Ignoring air resistance, the length of the projectile's path is given by
$$
L(\theta)=\frac{v_0^2}{32}\left[\sin \theta-(\cos \theta)^2 \cdot\left(\ln \left[\tan \left(\frac{\pi-2 \theta}{4}\right)\right]\right)\right]
$$
where $0<\theta<\frac{\pi}{2}$.
(a) Find the length of the object's path for angles $\theta=\frac{\pi}{6}, \frac{\pi}{4}$, and $\frac{\pi}{3}$ if the initial velocity is 128 feet per second.
(b) Using a graphing utility, determine the angle required for the object to have a path length of 550 feet if the initial velocity is 128 feet per second.
(c) What angle will result in the longest path? How does this angle compare to the angle that results in the longest range? (See Problems 121-124.)

Ziya Ogron
Ziya Ogron
Numerade Educator
01:51

Problem 133

Establish the identity:
$$
(\sin \theta \cos \phi)^2+(\sin \theta \sin \phi)^2+\cos ^2 \theta=1
$$

Amit Srivastava
Amit Srivastava
Numerade Educator
01:22

Problem 134

Are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

Solve: $5 x^2+2=5-14 x$

Dharmendra Jain
Dharmendra Jain
Numerade Educator
00:34

Problem 134

The length $L$ of the chord joining the endpoints of an arc on a circle of radius $r$ subtended by a central angle $\theta$, $0<\theta \leq \pi$, is given by $L=r \sqrt{2-2 \cos \theta}$. Use this fact to approximate the field width (the width of scenery the lens can image) of a $450 \mathrm{~mm}$ camera lens at a distance of 920 feet if the viewing angle of the lens is $\frac{\pi}{30}$.

AG
Ankit Gupta
Numerade Educator
02:26

Problem 134

If $2 \sin ^2 \theta+3 \cos ^2 \theta=3 \sin \theta \cos \theta+1$ with $\theta$ in quadrant $\mathrm{I}$, find the possible values for $\cot \theta$.

Yujie Wang
Yujie Wang
College of San Mateo
06:24

Problem 135

Are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

Write the function that is finally graphed if the following transformations are applied in order to the graph of $y=|x|$.
1. Shift left 3 units.
2. Reflect about the $x$-axis.
3. Shift down 4 units.

Jaymie Irwin
Jaymie Irwin
Numerade Educator
10:15

Problem 135

An object is propelled upward at an angle $\theta$, $45^{\circ}<\theta<90^{\circ}$, to the horizontal with an initial velocity of $v_0$ feet per second from the base of an inclined plane that makes an angle of $45^{\circ}$ with the horizontal. See the figure.
(Figure can't copy)
If air resistance is ignored, the distance $R$ that it travels up the inclined plane as a function of $\theta$ is given by
$$
R(\theta)=\frac{v_0^2 \sqrt{2}}{32}[\sin (2 \theta)-\cos (2 \theta)-1]
$$
(a) Find the distance $R$ that the object travels along the inclined plane if the initial velocity is 32 feet per second and $\theta=60^{\circ}$.
(b) Graph $R=R(\theta)$ if the initial velocity is 32 feet per second.
(c) What value of $\theta$ makes $R$ largest?

Linda Hand
Linda Hand
Numerade Educator
02:29

Problem 135

If $\sin (4 \theta)=\cos (2 \theta)$ and $0<4 \theta<\frac{\pi}{2}$, find the exact value of $\sin (8 \theta)+\cot (4 \theta)-2$.

Abdul Vahid M
Abdul Vahid M
Numerade Educator
08:31

Problem 136

Are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

Find the horizontal and vertical asymptotes of $R(x)=\frac{3 x^2-12}{x^2-5 x-14}$.

Jaymie Irwin
Jaymie Irwin
Numerade Educator
03:10

Problem 136

If $\theta, 0<\theta<\pi$, is the angle between the positive $x$-axis and a nonhorizontal, nonvertical line $L$, show that the slope $m$ of $L$ equals $\tan \theta$. The angle $\theta$ is called the inclination of $L$.

Yujie Wang
Yujie Wang
College of San Mateo
02:16

Problem 136

If $\tan \theta=3-\sec \theta$ with $\theta$ in quadrant $\mathrm{I}$, what is $\sin \theta+\cos \theta$ ?

Abdul Vahid M
Abdul Vahid M
Numerade Educator
01:48

Problem 137

Are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

Find $c$ so the points $(2, c)$ and $(-1,4)$ are on a line perpendicular to $2 x-y=5$.

Aman Gupta
Aman Gupta
Numerade Educator
03:08

Problem 137

Use the figure to approximate the value of the six trigonometric functions at to the nearest tenth. Then use a calculator to approximate each of the six trigonometric functions at $t$.

(a) $t=2$
(b) $t=4$

Sheryl Ezze
Sheryl Ezze
Numerade Educator
02:47

Problem 137

Find the exact value of $\sin \theta-\cos \theta$ if $\cos \theta-8 \sin \theta=7$ and $180^{\circ}<\theta<270^{\circ}$.

AG
Ankit Gupta
Numerade Educator
01:33

Problem 138

Are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

Solve: $2 \sqrt{x-3}+5=8$

Eleanor Johnson
Eleanor Johnson
Numerade Educator
03:12

Problem 138

Use the figure to approximate the value of the six trigonometric functions at to the nearest tenth. Then use a calculator to approximate each of the six trigonometric functions at $t$.

(a) $t=1$
(b) $t=5.1$

Anna Jones
Anna Jones
Numerade Educator
04:40

Problem 138

Write down five properties of the tangent function. Explain the meaning of each.

Amit Srivastava
Amit Srivastava
Numerade Educator
01:25

Problem 139

Are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

Find the domain of $h(x)=\frac{3 x}{x^2-9}$.

Kian Manafi
Kian Manafi
Numerade Educator
03:56

Problem 139

Let $\theta$ be the measure of an angle, in radians, in standard position with $\frac{\pi}{2}<\theta<\pi$. Find the exact $x$-coordinate of the intersection of the terminal side of $\theta$ with the unit circle, given $\cos ^2 \theta-\sin \theta=-\frac{1}{9}$. State the answer as a single fraction, completely simplified, with rationalized denominator.

Abdul Vahid M
Abdul Vahid M
Numerade Educator
01:25

Problem 139

Describe your understanding of the meaning of a periodic function.

Amit Srivastava
Amit Srivastava
Numerade Educator
01:22

Problem 140

Are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

Find the difference quotient of $f(x)=2 x^3-5$.

Eleanor Johnson
Eleanor Johnson
Numerade Educator
03:56

Problem 140

Let $\theta$ be the measure of an angle, in radians, in standard position with $\pi<\theta<\frac{3 \pi}{2}$. Find the exact $y$-coordinate of the intersection of the terminal side of $\theta$ with the unit circle, given $\cos \theta+\sin ^2 \theta=\frac{19}{25}$. State the answer as a single fraction.

Abdul Vahid M
Abdul Vahid M
Numerade Educator
00:55

Problem 140

Explain how to find the value of $\sin 390^{\circ}$ using periodic properties.

Amit Srivastava
Amit Srivastava
Numerade Educator
02:11

Problem 141

Are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

Multiply: $(3 x-2)^3$

Elizabeth Waters
Elizabeth Waters
Numerade Educator
01:30

Problem 141

If the terminal side of an angle contains the point $(5 n,-12 n)$ with $n>0$, find $\sin \theta$.

RM
Rachel Maslow
Numerade Educator
00:51

Problem 141

Explain how to find the value of $\cos \left(-45^{\circ}\right)$ using even-odd properties.

Amit Srivastava
Amit Srivastava
Numerade Educator
01:24

Problem 142

Are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

Use a graphing utility to determine the interval(s) where $g(x)=3.2 x^4-5.3 x^2+2 x-1$ is decreasing.

Mrinal Rana
Mrinal Rana
Numerade Educator
03:00

Problem 142

Write a brief paragraph that explains how to quickly compute the trigonometric functions of $30^{\circ}, 45^{\circ}$, and $60^{\circ}$.

Ethan Somes
Ethan Somes
Numerade Educator
02:29

Problem 142

Explain how to find the value of $\sin 390^{\circ}$ and $\cos \left(-45^{\circ}\right)$ using the unit circle.

Amit Srivastava
Amit Srivastava
Numerade Educator
01:38

Problem 143

Write a brief paragraph that explains how to quickly compute the trigonometric functions of $0^{\circ}, 90^{\circ}, 180^{\circ}$, and $270^{\circ}$.

Sheryl Ezze
Sheryl Ezze
Numerade Educator
00:55

Problem 143

Are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

Given: $f(x)=x^2-3$ and $g(x)=x-7$, find $(f \circ g)(x)$.

Steven Clarke
Steven Clarke
Numerade Educator
00:29

Problem 144

How would you explain the meaning of the sine function to a fellow student who has just completed college algebra?

Khanh Ha
Khanh Ha
Numerade Educator
02:02

Problem 144

Are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

Graph $f(x)=-2 x^2+12 x-13$ using transformations. Find the vertex and the axis of symmetry.

Allison Knapp
Allison Knapp
Numerade Educator
06:00

Problem 145

Draw a unit circle. Label the angles $0, \frac{\pi}{6}, \frac{\pi}{4}, \frac{\pi}{3}, \ldots, \frac{7 \pi}{4}$, $\frac{11 \pi}{6}, 2 \pi$ and the coordinates of the points on the unit circle that correspond to each of these angles. Explain how symmetry can be used to find the coordinates of points on the unit circle for angles whose terminal sides are in quadrants II, III, and IV.

Sheryl Ezze
Sheryl Ezze
Numerade Educator
01:02

Problem 145

Are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

Solve exactly: $e^{x-4}=6$

Eleanor Johnson
Eleanor Johnson
Numerade Educator
00:30

Problem 146

Are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

Find the domain of $f(x)=\ln (5 x+2)$.

James Kiss
James Kiss
Numerade Educator
01:36

Problem 146

Are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

Find the real zeros of $f(x)=x^3-9 x^2+3 x-27$.

Eleanor Johnson
Eleanor Johnson
Numerade Educator
View

Problem 147

Are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

If the polynomial function $P(x)=x^4-5 x^3-9 x^2+155 x-250$ has zeros of $4+3 i$ and 2 , find the remaining zeros of the function.

Nicole Hoffman
Nicole Hoffman
Numerade Educator
01:33

Problem 147

Are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

Solve: $\sqrt{x+2}-\sqrt{x-5}=2$

Eleanor Johnson
Eleanor Johnson
Numerade Educator
01:23

Problem 148

Are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

Find the remainder when $P(x)=8 x^4-2 x^3+x-8$ is divided by $x+2$.

Naresh Bagrecha
Naresh Bagrecha
Numerade Educator
01:37

Problem 148

Are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

If the real zeros of $g(x)$ are -2 and 3 , what are the real zeros of $g(x+6)$ ?

Eleanor Johnson
Eleanor Johnson
Numerade Educator
03:29

Problem 149

Are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

Sidewalk Area A sidewalk with a uniform width of 3 feet is to be placed around a circular garden with a diameter of 24 feet. Find the exact area of the sidewalk.

Khanh Ha
Khanh Ha
Numerade Educator
01:24

Problem 149

Are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

Solve: $\log _4(x-5)=2$

Yujie Wang
Yujie Wang
College of San Mateo
01:36

Problem 150

Are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

Find the real zeros of $f(x)=3 x^2-7 x-9$.

Eleanor Johnson
Eleanor Johnson
Numerade Educator
02:03

Problem 150

Are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

Find $c$ so that $f(x)=6 x^2-28 x+c$ has a minimum value of $\frac{7}{3}$.

Eleanor Johnson
Eleanor Johnson
Numerade Educator
01:30

Problem 151

Are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

If $g(x)=\frac{1}{x^2+1}$, find $f(x)$ so that $f(g(x))=\frac{x^2+1}{2}$.

Jennifer Stoner
Jennifer Stoner
Numerade Educator
01:25

Problem 151

Are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

Find the intercepts of the graph of $-3 x+5 y=15$.

Eleanor Johnson
Eleanor Johnson
Numerade Educator
View

Problem 152

Are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

If $f(x)=x^2-3$ and $g(x)=-x+3$, determine where $g(x) \geq f(x)$.

Nicole Hoffman
Nicole Hoffman
Numerade Educator
01:22

Problem 152

Are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

Find the difference quotient for $f(x)=\frac{3}{2} x^2-5 x+1$

Eleanor Johnson
Eleanor Johnson
Numerade Educator
04:04

Problem 153

Are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

Solve int $(x+3)=-2$.

Christine Anacker
Christine Anacker
Numerade Educator
01:26

Problem 154

Are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

If the point $(3,-4)$ is on the graph of $y=f(x)$, what corresponding point must be on the graph of $\frac{1}{2} f(x-3)$ ?

Raushan Kumar
Raushan Kumar
Numerade Educator
02:26

Problem 155

Are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

If $g(x)=\frac{x^2}{4}-\frac{1}{x^2}$, simplify $\sqrt{1+[g(x)]^2}$.

Yujie Wang
Yujie Wang
College of San Mateo