Precalculus

Robert Blitzer

Chapter 4

Trigonometric Functions - all with Video Answers

Educators

+ 11 more educators

Section 1

Angles and Radian Measure

Problem 1

In Exercises $1-6,$ the measure of an angle is given. Classify the angle as acute, right, obtuse, or straight.
$$
135^{\circ}
$$

Linh Vu

Linh Vu

Numerade Educator

Problem 2

In Exercises $1-6,$ the measure of an angle is given. Classify the angle as acute, right, obtuse, or straight.
$$
177^{\circ}
$$

Mukesh Devi

Numerade Educator

Problem 3

In Exercises $1-6,$ the measure of an angle is given. Classify the angle as acute, right, obtuse, or straight.
$$
83.135^{\circ}
$$

Suman Saurav Thakur

Suman Saurav Thakur

Numerade Educator

Problem 4

In Exercises $1-6,$ the measure of an angle is given. Classify the angle as acute, right, obtuse, or straight.
$$
87.177^{\circ}
$$

Linh Vu

Numerade Educator

Problem 5

In Exercises $1-6,$ the measure of an angle is given. Classify the angle as acute, right, obtuse, or straight.
$$
\pi
$$

Linh Vu

Numerade Educator

Problem 6

In Exercises $1-6,$ the measure of an angle is given. Classify the angle as acute, right, obtuse, or straight.
$$
\frac{\pi}{2}
$$

AG

Ankit Gupta

Numerade Educator

Problem 7

In Exercises $7-12,$ find the radian measure of the central angle of a circle of radius $r$ that intercepts an arc of length $s .$
$$\begin{array}{ll}{\text { Radius, } r} & {\text { Are Length,s }} \\ {10 \text { inches }} & {40 \text { inches }}\end{array}$$

Nolwazi Dube

Numerade Educator

Problem 8

In Exercises $7-12,$ find the radian measure of the central angle of a circle of radius $r$ that intercepts an arc of length $s .$
$$\begin{array}{ll}{\text { Radius, } r} & {\text { Are Length,s }} \\ {5 \text { feet }} & {30 \text { feet }}\end{array}$$

Sheryl Ezze

Numerade Educator

Problem 9

In Exercises $7-12,$ find the radian measure of the central angle of a circle of radius $r$ that intercepts an arc of length $s .$
$$\begin{array}{ll}{\text { Radius, } r} & {\text { Are Length,s }} \\ {6 \text { yards }} & {8 \text { yards }}\end{array}$$

Sheryl Ezze

Numerade Educator

Problem 10

In Exercises $7-12,$ find the radian measure of the central angle of a circle of radius $r$ that intercepts an arc of length $s .$
$$\begin{array}{ll}{\text { Radius, } r} & {\text { Are Length,s }} \\ {8 \text { yards }} & {18 \text { yards }}\end{array}$$

Linh Vu

Numerade Educator

Problem 11

In Exercises $7-12,$ find the radian measure of the central angle of a circle of radius $r$ that intercepts an arc of length $s .$
$$\begin{array}{ll}{\text { Radius, } r} & {\text { Are Length,s }} \\ {1 \text { meter }} & {400 \text { centimeters }}\end{array}$$

Linh Vu

Numerade Educator

Problem 12

In Exercises $7-12,$ find the radian measure of the central angle of a circle of radius $r$ that intercepts an arc of length $s .$
$$\begin{array}{ll}{\text { Radius, } r} & {\text { Are Length,s }} \\ {1 \text { meter }} & {600 \text { centimeters }}\end{array}$$

Linh Vu

Numerade Educator

Problem 13

In Exercises $13-20,$ convert each angle in degrees to radians. Express your answer as a multiple of $\pi .$
$$
45^{\circ}
$$

Gregory Higby

Numerade Educator

Problem 14

In Exercises $13-20,$ convert each angle in degrees to radians. Express your answer as a multiple of $\pi .$
$$
18^{\circ}
$$

Linh Vu

Numerade Educator

Problem 15

In Exercises $13-20,$ convert each angle in degrees to radians. Express your answer as a multiple of $\pi .$
$$
135^{\circ}
$$

Linh Vu

Numerade Educator

Problem 16

In Exercises $13-20,$ convert each angle in degrees to radians. Express your answer as a multiple of $\pi .$
$$
150^{\circ}
$$

Linh Vu

Numerade Educator

Problem 17

In Exercises $13-20,$ convert each angle in degrees to radians. Express your answer as a multiple of $\pi .$
$$
300^{\circ}
$$

Linh Vu

Numerade Educator

Problem 18

In Exercises $13-20,$ convert each angle in degrees to radians. Express your answer as a multiple of $\pi .$
$$
330^{\circ}
$$

Ma. Theresa Alin

Ma. Theresa Alin

Numerade Educator

Problem 19

In Exercises $13-20,$ convert each angle in degrees to radians. Express your answer as a multiple of $\pi .$
$$
-225^{\circ}
$$

Sheryl Ezze

Numerade Educator

Problem 20

In Exercises $13-20,$ convert each angle in degrees to radians. Express your answer as a multiple of $\pi .$
$$
-270^{\circ}
$$

Linh Vu

Numerade Educator

Problem 21

In Exercises $21-28,$ convert each angle in radians to degrees.
$$
\frac{\pi}{2}
$$

Linh Vu

Numerade Educator

Problem 22

In Exercises $21-28,$ convert each angle in radians to degrees.
$$
\frac{\pi}{9}
$$

Linh Vu

Numerade Educator

Problem 23

In Exercises $21-28,$ convert each angle in radians to degrees.
$$
\frac{2 \pi}{3}
$$

Linh Vu

Numerade Educator

Problem 24

In Exercises $21-28,$ convert each angle in radians to degrees.
$$
\frac{3 \pi}{4}
$$

Linh Vu

Numerade Educator

Problem 25

In Exercises $21-28,$ convert each angle in radians to degrees.
$$
\frac{7 \pi}{6}
$$

Linh Vu

Numerade Educator

Problem 26

In Exercises $21-28,$ convert each angle in radians to degrees.
$$
\frac{11 \pi}{6}
$$

Linh Vu

Numerade Educator

Problem 27

In Exercises $21-28,$ convert each angle in radians to degrees.
$$
-3 \pi
$$

Linh Vu

Numerade Educator

Problem 28

In Exercises $21-28,$ convert each angle in radians to degrees.
$$
-4 \pi
$$

Linh Vu

Numerade Educator

Problem 29

In Exercises $29-34,$ convert each angle in degrees to radians. Round to two decimal places.
$$
18^{\circ}
$$

Linh Vu

Numerade Educator

Problem 30

In Exercises $29-34,$ convert each angle in degrees to radians. Round to two decimal places.
$$
76^{\circ}
$$

Linh Vu

Numerade Educator

Problem 31

In Exercises $29-34,$ convert each angle in degrees to radians. Round to two decimal places.
$$
-40^{\circ}
$$

Linh Vu

Numerade Educator

Problem 32

In Exercises $29-34,$ convert each angle in degrees to radians. Round to two decimal places.
$$
-50^{\circ}
$$

Justin Swantek

Numerade Educator

Problem 33

In Exercises $29-34,$ convert each angle in degrees to radians. Round to two decimal places.
$$
200^{\circ}
$$

Linh Vu

Numerade Educator

Problem 34

In Exercises $29-34,$ convert each angle in degrees to radians. Round to two decimal places.
$$
250^{\circ}
$$

Sheryl Ezze

Numerade Educator

Problem 35

In Exercises $35-40,$ convert each angle in radians to degrees. Round to two decimal places.
2 radians

Linh Vu

Numerade Educator

Problem 36

In Exercises $35-40,$ convert each angle in radians to degrees. Round to two decimal places.
3 radians

Linh Vu

Numerade Educator

Problem 37

In Exercises $35-40,$ convert each angle in radians to degrees. Round to two decimal places.
$\frac{\pi}{13}$ radians

Linh Vu

Numerade Educator

Problem 38

In Exercises $35-40,$ convert each angle in radians to degrees. Round to two decimal places.
$\frac{\pi}{17}$ radians

Linh Vu

Numerade Educator

Problem 39

In Exercises $35-40,$ convert each angle in radians to degrees. Round to two decimal places.
$-4.8$ radians

Linh Vu

Numerade Educator

Problem 40

In Exercises $35-40,$ convert each angle in radians to degrees. Round to two decimal places.
$-5.2$ radians

Linh Vu

Numerade Educator

Problem 41

In Exercises $41-56$ , use the circle shown in the rectangular coordinate system to draw each angle in standard position. State the quadrant in which the angle lies. When an angle's measure is given in radians, work the exercise without converting to degrees.
$$
\frac{7 \pi}{6}
$$

Linh Vu

Numerade Educator

Problem 42

In Exercises $41-56$ , use the circle shown in the rectangular coordinate system to draw each angle in standard position. State the quadrant in which the angle lies. When an angle's measure is given in radians, work the exercise without converting to degrees.
$$
\frac{4 \pi}{3}
$$

Linh Vu

Numerade Educator

Problem 43

In Exercises $41-56$ , use the circle shown in the rectangular coordinate system to draw each angle in standard position. State the quadrant in which the angle lies. When an angle's measure is given in radians, work the exercise without converting to degrees.
$$
\frac{3 \pi}{4}
$$

Linh Vu

Numerade Educator

Problem 44

In Exercises $41-56$ , use the circle shown in the rectangular coordinate system to draw each angle in standard position. State the quadrant in which the angle lies. When an angle's measure is given in radians, work the exercise without converting to degrees.
$$
\frac{7 \pi}{4}
$$

Linh Vu

Numerade Educator

Problem 45

In Exercises $41-56$ , use the circle shown in the rectangular coordinate system to draw each angle in standard position. State the quadrant in which the angle lies. When an angle's measure is given in radians, work the exercise without converting to degrees.
$$
-\frac{2 \pi}{3}
$$

Linh Vu

Numerade Educator

Problem 46

In Exercises $41-56$ , use the circle shown in the rectangular coordinate system to draw each angle in standard position. State the quadrant in which the angle lies. When an angle's measure is given in radians, work the exercise without converting to degrees.
$$
-\frac{5 \pi}{6}
$$

Linh Vu

Numerade Educator

Problem 47

In Exercises $41-56$ , use the circle shown in the rectangular coordinate system to draw each angle in standard position. State the quadrant in which the angle lies. When an angle's measure is given in radians, work the exercise without converting to degrees.
$$
-\frac{5 \pi}{4}
$$

Linh Vu

Numerade Educator

Problem 48

In Exercises $41-56$ , use the circle shown in the rectangular coordinate system to draw each angle in standard position. State the quadrant in which the angle lies. When an angle's measure is given in radians, work the exercise without converting to degrees.
$$
-\frac{7 \pi}{4}
$$

Linh Vu

Numerade Educator

Problem 49

In Exercises $41-56$ , use the circle shown in the rectangular coordinate system to draw each angle in standard position. State the quadrant in which the angle lies. When an angle's measure is given in radians, work the exercise without converting to degrees.
$$
\frac{16 \pi}{3}
$$

Linh Vu

Numerade Educator

Problem 50

In Exercises $41-56$ , use the circle shown in the rectangular coordinate system to draw each angle in standard position. State the quadrant in which the angle lies. When an angle's measure is given in radians, work the exercise without converting to degrees.
$$
\frac{14 \pi}{3}
$$

Linh Vu

Numerade Educator

Problem 51

In Exercises $41-56$ , use the circle shown in the rectangular coordinate system to draw each angle in standard position. State the quadrant in which the angle lies. When an angle's measure is given in radians, work the exercise without converting to degrees.
$$
120^{\circ}
$$

Linh Vu

Numerade Educator

Problem 52

In Exercises $41-56$ , use the circle shown in the rectangular coordinate system to draw each angle in standard position. State the quadrant in which the angle lies. When an angle's measure is given in radians, work the exercise without converting to degrees.
$$
150^{\circ}
$$

Linh Vu

Numerade Educator

Problem 53

In Exercises $41-56$ , use the circle shown in the rectangular coordinate system to draw each angle in standard position. State the quadrant in which the angle lies. When an angle's measure is given in radians, work the exercise without converting to degrees.
$$
-210^{\circ}
$$

Linh Vu

Numerade Educator

Problem 54

In Exercises $41-56$ , use the circle shown in the rectangular coordinate system to draw each angle in standard position. State the quadrant in which the angle lies. When an angle's measure is given in radians, work the exercise without converting to degrees.
$$
-240^{\circ}
$$

Linh Vu

Numerade Educator

Problem 55

In Exercises $41-56$ , use the circle shown in the rectangular coordinate system to draw each angle in standard position. State the quadrant in which the angle lies. When an angle's measure is given in radians, work the exercise without converting to degrees.
$$
420^{\circ}
$$

Linh Vu

Numerade Educator

Problem 56

In Exercises $41-56$ , use the circle shown in the rectangular coordinate system to draw each angle in standard position. State the quadrant in which the angle lies. When an angle's measure is given in radians, work the exercise without converting to degrees.
$$
405^{\circ}
$$

Linh Vu

Numerade Educator

Problem 57

In Exercises $57-70,$ find a positive angle less than $360^{\circ}$ or 2$\pi$ that is coterminal with the given angle.
$$
395^{\circ}
$$

Linh Vu

Numerade Educator

Problem 58

In Exercises $57-70,$ find a positive angle less than $360^{\circ}$ or 2$\pi$ that is coterminal with the given angle.
$$
415^{\circ}
$$

Linh Vu

Numerade Educator

Problem 59

In Exercises $57-70,$ find a positive angle less than $360^{\circ}$ or 2$\pi$ that is coterminal with the given angle.
$$
-150^{\circ}
$$

Linh Vu

Numerade Educator

Problem 60

In Exercises $57-70,$ find a positive angle less than $360^{\circ}$ or 2$\pi$ that is coterminal with the given angle.
$$
-160^{\circ}
$$

Linh Vu

Numerade Educator

Problem 61

In Exercises $57-70,$ find a positive angle less than $360^{\circ}$ or 2$\pi$ that is coterminal with the given angle.
$$
-765^{\circ}
$$

Linh Vu

Numerade Educator

Problem 62

In Exercises $57-70,$ find a positive angle less than $360^{\circ}$ or 2$\pi$ that is coterminal with the given angle.
$$
-760^{\circ}
$$

Linh Vu

Numerade Educator

Problem 63

In Exercises $57-70,$ find a positive angle less than $360^{\circ}$ or 2$\pi$ that is coterminal with the given angle.
$$
\frac{19 \pi}{6}
$$

Linh Vu

Numerade Educator

Problem 64

In Exercises $57-70,$ find a positive angle less than $360^{\circ}$ or 2$\pi$ that is coterminal with the given angle.
$$
\frac{17 \pi}{5}
$$

Linh Vu

Numerade Educator

Problem 65

In Exercises $57-70,$ find a positive angle less than $360^{\circ}$ or 2$\pi$ that is coterminal with the given angle.
$$
\frac{23 \pi}{5}
$$

Linh Vu

Numerade Educator

Problem 66

In Exercises $57-70,$ find a positive angle less than $360^{\circ}$ or 2$\pi$ that is coterminal with the given angle.
$$
\frac{25 \pi}{6}
$$

Linh Vu

Numerade Educator

Problem 67

In Exercises $57-70,$ find a positive angle less than $360^{\circ}$ or 2$\pi$ that is coterminal with the given angle.
$$
-\frac{\pi}{50}
$$

Linh Vu

Numerade Educator

Problem 68

In Exercises $57-70,$ find a positive angle less than $360^{\circ}$ or 2$\pi$ that is coterminal with the given angle.
$$
-\frac{\pi}{40}
$$

Linh Vu

Numerade Educator

Problem 69

In Exercises $57-70,$ find a positive angle less than $360^{\circ}$ or 2$\pi$ that is coterminal with the given angle.
$$
-\frac{31 \pi}{7}
$$

Linh Vu

Numerade Educator

Problem 70

In Exercises $57-70,$ find a positive angle less than $360^{\circ}$ or 2$\pi$ that is coterminal with the given angle.
$$
-\frac{38 \pi}{9}
$$

Linh Vu

Numerade Educator

Problem 71

In Exercises $71-74,$ find the length of the arc on a circle of radius $r$ intercepted by a central angle $\theta .$ Express arc length in terms of $\pi .$ Then round your answer to two decimal places.
$$\begin{array}{ll}{\text { Radius, } r} & {\text { Central Angle, } \theta} \\ {12 \text { inches }} & {\theta=45^{\circ}}\end{array}$$

Linh Vu

Numerade Educator

Problem 72

Find the length of the arc on a circle of radius $r$ intercepted by a central angle $\theta .$ Express arc length in terms of $\pi .$ Then round your answer to two decimal places.
$$\begin{array}{ll}{\text { Radius, } r} & {\text { Central Angle, } \theta} \\ {16 \text { inches }} & {\theta=60^{\circ}}\end{array}$$

Nolwazi Dube

Numerade Educator

Problem 73

In Exercises $71-74,$ find the length of the arc on a circle of radius $r$ intercepted by a central angle $\theta .$ Express arc length in terms of $\pi .$ Then round your answer to two decimal places.
$$\begin{array}{ll}{\text { Radius, } r} & {\text { Central Angle, } \theta} \\ {8 \text { feet }} & {\theta=225^{\circ}}\end{array}$$

Linh Vu

Numerade Educator

Problem 74

In Exercises $71-74,$ find the length of the arc on a circle of radius $r$ intercepted by a central angle $\theta .$ Express arc length in terms of $\pi .$ Then round your answer to two decimal places.
$$\begin{array}{ll}{\text { Radius, } r} & {\text { Central Angle, } \theta} \\ {9 \text { yards }} & {\theta=315^{\circ}}\end{array}$$

Sheryl Ezze

Numerade Educator

Problem 75

In Exercises $75-76,$ express each angular speed in radians per second.
6 revolutions per second

Sheryl Ezze

Numerade Educator

Problem 76

In Exercises $75-76,$ express each angular speed in radians per second.
20 revolutions per second

Linh Vu

Numerade Educator

Problem 77

Use the circle shown in the rectangular coordinate system to solve Exercises $77-82 .$ Find two angles, in radians, between $-2 \pi$ and 2$\pi$ such that each angle's terminal side passes through the origin and the given point.
A

Linh Vu

Numerade Educator

Problem 78

Use the circle shown in the rectangular coordinate system to solve Exercises $77-82 .$ Find two angles, in radians, between $-2 \pi$ and 2$\pi$ such that each angle's terminal side passes through the origin and the given point.
B

Linh Vu

Numerade Educator

Problem 79

Use the circle shown in the rectangular coordinate system to solve Exercises $77-82 .$ Find two angles, in radians, between $-2 \pi$ and 2$\pi$ such that each angle's terminal side passes through the origin and the given point.
D

Linh Vu

Numerade Educator

Problem 80

Use the circle shown in the rectangular coordinate system to solve Exercises $77-82 .$ Find two angles, in radians, between $-2 \pi$ and 2$\pi$ such that each angle's terminal side passes through the origin and the given point.
F

Linh Vu

Numerade Educator

Problem 81

Use the circle shown in the rectangular coordinate system to solve Exercises $77-82 .$ Find two angles, in radians, between $-2 \pi$ and 2$\pi$ such that each angle's terminal side passes through the origin and the given point.
E

Linh Vu

Numerade Educator

Problem 82

Use the circle shown in the rectangular coordinate system to solve Exercises $77-82 .$ Find two angles, in radians, between $-2 \pi$ and 2$\pi$ such that each angle's terminal side passes through the origin and the given point.
C

Linh Vu

Numerade Educator

Problem 83

In Exercises $83-86,$find the positive radian measure of the angle that the second hand of a clock moves through in the given time.
55 seconds

Linh Vu

Numerade Educator

Problem 84

In Exercises $83-86,$find the positive radian measure of the angle that the second hand of a clock moves through in the given time.
35 seconds

Linh Vu

Numerade Educator

Problem 85

In Exercises $83-86,$find the positive radian measure of the angle that the second hand of a clock moves through in the given time.
3 minutes and 40 seconds

Linh Vu

Numerade Educator

Problem 86

In Exercises $83-86,$find the positive radian measure of the angle that the second hand of a clock moves through in the given time.
4 minutes and 25 seconds

Linh Vu

Numerade Educator

Problem 87

The minute hand of a clock moves from 12 to 2 o'clock, or $\frac{1}{6}$ of a complete revolution. Through how many degrees does it move? Through how many radians does it move?

Babita Kumari

Numerade Educator

Problem 88

The minute hand of a clock moves from 12 to 4 o'clock, or $\frac{1}{3}$ of a complete revolution. Through how many degrees does it move? Through how many radians does it move?

Linh Vu

Numerade Educator

Problem 89

The minute hand of a clock is 8 inches long and moves from 12 to 2 o'clock. How far does the tip of the minute hand move? Express your answer in terms of $\pi$ and then round to two decimal places.

Ashley Boni

Numerade Educator

Problem 90

The minute hand of a clock is 6 inches long and moves from 12 to 4 o'clock. How far does the tip of the minute hand move? Express your answer in terms of $\pi$ and then round to two decimal places.

Khushbu Rani

Numerade Educator

Problem 91

The figure shows a highway sign that warns of a railway crossing. The lines that form the cross pass through the circle's center and intersect at right angles. If the radius of the circle is 24 inches, find the length of each of the four arcs formed by the cross. Express your answer in terms of $\pi$ and then round to two decimal places.

Linh Vu

Numerade Educator

Problem 92

The radius of a wheel rolling on the ground is 80 centimeters. If the wheel rotates through an angle of $60^{\circ},$ how many centimeters does it move? Express your answer in terms of $\pi$ and then round to two decimal places.

Anthony Han

Numerade Educator

Problem 93

How do we measure the distance between two points, A and B, on Earth? We measure along a circle with a center, C, at the center of Earth. The radius of the circle is equal to the distance from C to the surface. Use the fact that Earth is a sphere of radius equal to approximately 4000 miles to solve Exercises 93–96.
If two points, $A$ and $B,$ are 8000 miles apart, express angle $\theta$ in radians and in degrees.

Sheryl Ezze

Numerade Educator

Problem 94

How do we measure the distance between two points, A and B, on Earth? We measure along a circle with a center, C, at the center of Earth. The radius of the circle is equal to the distance from C to the surface. Use the fact that Earth is a sphere of radius equal to approximately 4000 miles to solve Exercises 93–96.
If two points, $A$ and $B,$ are $10,000$ miles apart, express angle $\theta$ in radians and in degrees.

Linh Vu

Numerade Educator

Problem 95

How do we measure the distance between two points, A and B, on Earth? We measure along a circle with a center, C, at the center of Earth. The radius of the circle is equal to the distance from C to the surface. Use the fact that Earth is a sphere of radius equal to approximately 4000 miles to solve Exercises 93–96.
If $\theta=30^{\circ},$ find the distance between $A$ and $B$ to the nearest mile.

Linh Vu

Numerade Educator

Problem 96

How do we measure the distance between two points, A and B, on Earth? We measure along a circle with a center, C, at the center of Earth. The radius of the circle is equal to the distance from C to the surface. Use the fact that Earth is a sphere of radius equal to approximately 4000 miles to solve Exercises 93–96.
If $\theta=10^{\circ},$ find the distance between $A$ and $B$ to the nearest mile.

Linh Vu

Numerade Educator

Problem 97

The angular speed of a point on Earth is $\frac{\pi}{12}$ radian per hour. The Equator lies on a circle of radius approximately 4000 miles. Find the linear velocity, in miles per hour, of a point on the Equator.

Linh Vu

Numerade Educator

Problem 98

A Ferris wheel has a radius of 25 feet. The wheel is rotating at two revolutions per minute. Find the linear speed, in feet per minute, of a seat on this Ferris wheel.

Linh Vu

Numerade Educator

Problem 99

A water wheel has a radius of 12 feet. The wheel is rotating at 20 revolutions per minute. Find the linear speed, in feet per minute, of the water.

Darshan Maheshwari

Darshan Maheshwari

Numerade Educator

Problem 100

On a carousel, the outer row of animals is 20 feet from the center. The inner row of animals is 10 feet from the center. The carousel is rotating at 2.5 revolutions per minute. What is the difference, in feet per minute, in the linear speeds of the animals in the outer and inner rows? Round to the nearest foot per minute.

Linh Vu

Numerade Educator

Problem 101

What is an angle?

Linh Vu

Numerade Educator

Problem 102

What determines the size of an angle?

Linh Vu

Numerade Educator

Problem 103

Describe an angle in standard position.

Linh Vu

Numerade Educator

Problem 104

Explain the difference between positive and negative angles. What are coterminal angles?

Linh Vu

Numerade Educator

Problem 105

Explain what is meant by one radian.

Linh Vu

Numerade Educator

Problem 106

Explain how to find the radian measure of a central angle.

Linh Vu

Numerade Educator

Problem 107

Describe how to convert an angle in degrees to radians.

Linh Vu

Numerade Educator

Problem 108

Explain how to convert an angle in radians to degrees.

Linh Vu

Numerade Educator

Problem 109

Explain how to find the length of a circular arc.

Linh Vu

Numerade Educator

Problem 110

If a carousel is rotating at 2.5 revolutions per minute, explain how to find the linear speed of a child seated on one of the animals.

Linh Vu

Numerade Educator

Problem 111

The angular velocity of a point on Earth is $\frac{\pi}{12}$ radian per hour. Describe what happens every 24 hours.

Mukesh Devi

Numerade Educator

Problem 112

Have you ever noticed that we use the vocabulary of angles in everyday speech? Here is an example:
My opinion about art museums took a $180^{\circ}$ turn after visiting the San Francisco Museum of Modern Art. Explain what this means. Then give another example of the vocabulary of angles in everyday use.

AG

Ankit Gupta

Numerade Educator

Problem 113

In Exercises $113-116,$ use the keys on your calculator or graphing utility for converting an angle in degrees, minutes, and seconds $\left(D^{0} M^{\prime} S^{\prime \prime}\right)$ into decimal form, and vice versa.
In Exercises $113-114,$ convert each angle to a decimal in degrees. Round your answer to two decimal places.
$$
30^{\circ} 15^{\prime} 10^{\prime \prime}
$$

Linh Vu

Numerade Educator

Problem 114

In Exercises $113-116,$ use the keys on your calculator or graphing utility for converting an angle in degrees, minutes, and seconds $\left(D^{0} M^{\prime} S^{\prime \prime}\right)$ into decimal form, and vice versa.
In Exercises $113-114,$ convert each angle to a decimal in degrees. Round your answer to two decimal places.
$$
65^{\circ} 45^{\prime} 20^{\prime \prime}
$$

Linh Vu

Numerade Educator

Problem 115

In Exercises $115-116,$ convert each angle to $D^{\circ} M^{\prime} S^{\prime \prime}$ form. Round your answer to the nearest second.
$$
30.42^{\circ}
$$

Linh Vu

Numerade Educator

Problem 116

In Exercises $115-116,$ convert each angle to $D^{\circ} M^{\prime} S^{\prime \prime}$ form. Round your answer to the nearest second.
$$
50.42^{\circ}
$$

Linh Vu

Numerade Educator

Problem 117

Make Sense? In Exercises $117-120,$ determine whether each statement makes sense or does not make sense, and explain your reasoning.
I made an error because the angle I drew in standard position exceeded a straight angle.

Linh Vu

Numerade Educator

Problem 118

Make Sense? In Exercises $117-120,$ determine whether each statement makes sense or does not make sense, and explain your reasoning.
When an angle's measure is given in terms of $\pi,$ I know that it's measured using radians.

Linh Vu

Numerade Educator

Problem 119

Make Sense? In Exercises $117-120,$ determine whether each statement makes sense or does not make sense, and explain your reasoning.
When I convert degrees to radians, I multiply by $1,$ choosing $\frac{\pi}{180^{\circ}}$ for $1 .$

Linh Vu

Numerade Educator

Problem 120

Make Sense? In Exercises $117-120,$ determine whether each statement makes sense or does not make sense, and explain your reasoning.
Using radian measure, I can always find a positive angle less than 2$\pi$ coterminal with a given angle by adding or subtracting 2$\pi .$

Linh Vu

Numerade Educator

Problem 121

Using radian measure, I can always find a positive angle less than 2$\pi$ coterminal with a given angle by adding or subtracting 2$\pi .$

Linh Vu

Numerade Educator

Problem 122

A railroad curve is laid out on a circle. What radius should be used if the track is to change direction by $20^{\circ}$ in a distance of 100 miles? Round your answer to the nearest mile.

Linh Vu

Numerade Educator

Problem 123

Assuming Earth to be a sphere of radius 4000 miles, how many miles north of the Equator is Miami, Florida, if it is $26^{\circ}$ north from the Equator? Round your answer to the nearest mile.

Sheryl Ezze

Numerade Educator

Problem 124

Exercises $124-126$ will help you prepare for the material covered in the next section.
Graph: $x^{2}+y^{2}=1 .$ Then locate the point $\left(-\frac{1}{2}, \frac{\sqrt{3}}{2}\right)$ on the graph.

Linh Vu

Numerade Educator

Problem 125

Exercises $124-126$ will help you prepare for the material covered in the next section.
Use your graph of $x^{2}+y^{2}=1$ from Exercise 124 to determine the relation's domain and range.

Linh Vu

Numerade Educator

Problem 126

Exercises $124-126$ will help you prepare for the material covered in the next section.
Find $\frac{x}{y}$ for $x=-\frac{1}{2}$ and $y=\frac{\sqrt{3}}{2},$ and then rationalize the denominator.

Linh Vu

Numerade Educator