Algebra and Trigonometry

Michael Sullivan

Chapter 7

Trigonometric Functions - all with Video Answers

Educators

Section 1

Angles and Their Measure

Problem 1

Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red.
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 $r ?(\mathrm{p} .32)$

Vysakh M

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Problem 2

Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red.
If an object has a speed of $r$ feet per second and travels a ansed thes in in xomal, then $d=$ $(p p \cdot 138-139)$

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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.

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Problem 4

$\mathrm{A} \quad$ is a positive angle whose vertex is at the center of a circle.

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Problem 5

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
(b) minute
(a) degree
(c) second
(d) radian

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Problem 6

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

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Problem 7

$$\begin{array}{l}{180^{\circ}=\frac{\text { radians }}{2}} \\{\begin{array}{llll}{\text { (a) } \frac{\pi}{2}} & {\text { (b) } \pi} & {\text { (c) } \frac{3 \pi}{2}} & {\text { (d) } 2 \pi}\end{array}}\end{array}$$

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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 $v=\quad$ and the angular speed of the object is $\omega=$

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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 $t$

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Problem 10

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

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Problem 11

In Problems 11–22, draw each angle.
$$30^{\circ}$$

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Problem 12

In Problems 11–22, draw each angle.
$$60^{\circ}$$

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Problem 13

In Problems 11–22, draw each angle.
$$135^{\circ}$$

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Problem 14

In Problems 11–22, draw each angle.
$$-120^{\circ}$$

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Problem 15

In Problems 11–22, draw each angle.
$$5.450^{\circ}$$

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Problem 16

In Problems 11–22, draw each angle.
$$540^{\circ}$$

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Problem 17

In Problems 11–22, draw each angle.
$$\frac{3 \pi}{4}$$

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Problem 18

In Problems 11–22, draw each angle.
$$\frac{4 \pi}{3}$$

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Problem 19

In Problems 11–22, draw each angle.
$$-\frac{\pi}{6}$$

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Problem 20

In Problems 11–22, draw each angle.
$$-\frac{2 \pi}{3}$$

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Problem 21

In Problems 11–22, draw each angle.
$$30^{\circ}$$

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Problem 22

In Problems 11–22, draw each angle.
$$\frac{21 \pi}{4}$$

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Problem 23

In Problems 11–22, draw each angle.
$$30^{\circ}$$

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Problem 24

In Problems 11–22, draw each angle.
$$120^{\circ}$$

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Problem 25

In Problems 11–22, draw each angle.
$$240^{\circ}$$

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Problem 26

In Problems 11–22, draw each angle.
$$330^{\circ}$$

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Problem 27

In Problems 11–22, draw each angle.
$$-60^{\circ}$$

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Problem 28

In Problems 11–22, draw each angle.
$$-30^{\circ}$$

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Problem 29

In Problems 11–22, draw each angle.
$$180^{\circ}$$

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Problem 30

In Problems 11–22, draw each angle.
$$270^{\circ}$$

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Problem 31

In Problems 11–22, draw each angle.
$$-135^{\circ}$$

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Problem 32

In Problems 11–22, draw each angle.
$$-225^{\circ}$$

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Problem 33

In Problems 11–22, draw each angle.
$$-90^{\circ}$$

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Problem 34

In Problems 11–22, draw each angle.
$$-180^{\circ}$$

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Problem 35

In Problems 35–46, convert each angle in radians to degrees.
$$\frac{\pi}{3}$$

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Problem 36

In Problems 35–46, convert each angle in radians to degrees.
$$\frac{5 \pi}{6}$$

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Problem 37

In Problems 35–46, convert each angle in radians to degrees.
$$-\frac{5 \pi}{4}$$

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Problem 38

In Problems 35–46, convert each angle in radians to degrees.
$$-\frac{2 \pi}{3}$$

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Problem 39

In Problems 35–46, convert each angle in radians to degrees.
$$\frac{\pi}{2}$$

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Problem 40

In Problems 35–46, convert each angle in radians to degrees.
$$4 \pi$$

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Problem 41

In Problems 35–46, convert each angle in radians to degrees.
$$\frac{\pi}{12}$$

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Problem 42

In Problems 35–46, convert each angle in radians to degrees.
$$\frac{5 \pi}{12}$$

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Problem 43

In Problems 35–46, convert each angle in radians to degrees.
$$-\frac{\sqrt{11}}{2}$$

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Problem 44

In Problems 35–46, convert each angle in radians to degrees.
$$-\pi$$

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Problem 45

In Problems 35–46, convert each angle in radians to degrees.
$$-\frac{\pi}{6}$$

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Problem 46

In Problems 35–46, convert each angle in radians to degrees.
$$-\frac{3 \pi}{4}$$

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Problem 47

In Problems 47–52, convert each angle in degrees to radians. Express your answer in decimal form, rounded to two decimal places.
$$17^{\circ}$$

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Problem 48

In Problems 47–52, convert each angle in degrees to radians. Express your answer in decimal form, rounded to two decimal places.
$$73^{\circ}$$

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Problem 49

In Problems 47–52, convert each angle in degrees to radians. Express your answer in decimal form, rounded to two decimal places.
$$-40^{\circ}$$

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Problem 50

In Problems 47–52, convert each angle in degrees to radians. Express your answer in decimal form, rounded to two decimal places.
$$-51^{\circ}$$

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Problem 51

In Problems 47–52, convert each angle in degrees to radians. Express your answer in decimal form, rounded to two decimal places.
$$125^{\circ}$$

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Problem 52

In Problems 47–52, convert each angle in degrees to radians. Express your answer in decimal form, rounded to two decimal places.
$$350^{\circ}$$

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Problem 53

In Problems 53–58, convert each angle in radians to degrees. Express your answer in decimal form, rounded to two decimal places.
$$314$$

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Problem 54

In Problems 53–58, convert each angle in radians to degrees. Express your answer in decimal form, rounded to two decimal places.
$$0.75$$

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Problem 55

In Problems 53–58, convert each angle in radians to degrees. Express your answer in decimal form, rounded to two decimal places.
$$2$$

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Problem 56

In Problems 53–58, convert each angle in radians to degrees. Express your answer in decimal form, rounded to two decimal places.
$$3$$

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Problem 57

In Problems 53–58, convert each angle in radians to degrees. Express your answer in decimal form, rounded to two decimal places.
$$6.32$$

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Problem 58

In Problems 53–58, convert each angle in radians to degrees. Express your answer in decimal form, rounded to two decimal places.
$$\sqrt{2}$$

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Problem 59

In Problems 59–64, convert each angle to a decimal in degrees. Round your answer to two decimal places.
$$40^{\circ} 10^{\circ} 25^{\circ}$$

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Problem 60

In Problems 59–64, convert each angle to a decimal in degrees. Round your answer to two decimal places.
$$61^{\circ} 42^{\prime} 21^{=}$$

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Problem 61

In Problems 59–64, convert each angle to a decimal in degrees. Round your answer to two decimal places.
$$50^{\circ} 14^{\circ} 20^{\circ}$$

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Problem 62

In Problems 59–64, convert each angle to a decimal in degrees. Round your answer to two decimal places.
$$73^{\circ} 40^{\circ} 40^{-}$$

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Problem 63

In Problems 59–64, convert each angle to a decimal in degrees. Round your answer to two decimal places.
$$9^{\circ} 9^{\circ} 9^{\circ}$$

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Problem 64

In Problems 59–64, convert each angle to a decimal in degrees. Round your answer to two decimal places.
$$98^{\circ} 22^{\prime} 45^{\prime \prime}$$

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Problem 65

In Problems 65–70, convert each angle to D°M?S?? form. Round your answer to the nearest second.
$$40.32^{\circ}$$

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Problem 66

In Problems 65–70, convert each angle to D°M?S?? form. Round your answer to the nearest second.
$$61.24$$

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Problem 67

In Problems 65–70, convert each angle to D°M?S?? form. Round your answer to the nearest second.
$$18.255^{\circ}$$

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Problem 68

In Problems 65–70, convert each angle to D°M?S?? form. Round your answer to the nearest second.
$$29.411^{=}$$

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Problem 69

In Problems 65–70, convert each angle to D°M?S?? form. Round your answer to the nearest second.
$$19.99^{\circ}$$

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Problem 70

In Problems 65–70, convert each angle to D°M?S?? form. Round your answer to the nearest second.
$$44.01^{\circ}$$

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Problem 71

In Problems 71–78, s denotes the length of the arc of a circle of radius r subtended by the central angle u. Find the missing quantity. Round answers to three decimal places.
$$r=10 \text { meters, } \quad \theta=\frac{1}{2} \text { radian, } s=?$$

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Problem 72

In Problems 71–78, s denotes the length of the arc of a circle of radius r subtended by the central angle u. Find the missing quantity. Round answers to three decimal places.
$r=6$ feet, $\theta=2$ radians, $s=?$

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Problem 73

In Problems 71–78, s denotes the length of the arc of a circle of radius r subtended by the central angle u. Find the missing quantity. Round answers to three decimal places.
$$\theta=\frac{1}{3} \text { radian, } s=2 \text { feet, } r=?$$

Katelyn Chen

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Problem 74

In Problems 71–78, s denotes the length of the arc of a circle of radius r subtended by the central angle u. Find the missing quantity. Round answers to three decimal places.

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

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Problem 75

In Problems 71–78, s denotes the length of the arc of a circle of radius r subtended by the central angle u. Find the missing quantity. Round answers to three decimal places.
$$r=5 \text { miles, } s=3 \text { miles, } \quad \theta=?$$

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Problem 76

In Problems 71–78, s denotes the length of the arc of a circle of radius r subtended by the central angle u. Find the missing quantity. Round answers to three decimal places.
$$r=6 \text { meters, } \quad s=8 \text { meters, } \quad \theta=?$$

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Problem 77

In Problems 71–78, s denotes the length of the arc of a circle of radius r subtended by the central angle u. Find the missing quantity. Round answers to three decimal places.
$$r=2 \text { inches, } \theta=30^{\circ}, \quad s=?$$

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Problem 78

In Problems 71–78, s denotes the length of the arc of a circle of radius r subtended by the central angle u. Find the missing quantity. Round answers to three decimal places.
$$r=3 \text { meters, } \theta=120^{\circ}, \quad s=?$$

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Problem 79

In Problems $79-86,$ 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.
$$r=10 \text { meters, } \quad \theta=\frac{1}{2} \text { radian, } A=?$$

Katelyn Chen

Numerade Educator

Problem 80

In Problems $79-86,$ 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.
$$r=6 \text { feet, } \quad \theta=2 \text { radians, } \quad A=?$$

Katelyn Chen

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Problem 81

In Problems $79-86,$ 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.
$$\theta=\frac{1}{3} \text { radian, } A=2 \text { square feet, } r=?$$

Katelyn Chen

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Problem 82

In Problems $79-86,$ 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.
$$\theta=\frac{1}{4} \text { radian, } \quad A=6 \text { square centimeters, } \quad r=?$$

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Problem 83

In Problems $79-86,$ 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.
$r=5$ miles, $A=3$ square miles, $\theta=?$

Katelyn Chen

Numerade Educator

Problem 84

In Problems $79-86,$ 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.
$$r=6 \text { meters, } \quad A=8 \text { square meters, } \quad \theta=?$$

Katelyn Chen

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Problem 85

In Problems $79-86,$ 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.
$$r=2 \text { inches, } \theta=30^{\circ}, \quad A=?$$

Katelyn Chen

Numerade Educator

Problem 86

In Problems $79-86,$ 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.
$$r=3 \text { meters, } \quad \theta=120^{\circ}, \quad A=?$$

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Problem 87

In Problems 87–90, find the length s and the area A. Round answers to three decimal places.
(GRAPH CANT COPY)

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Problem 88

In Problems 87–90, find the length s and the area A. Round answers to three decimal places.
(GRAPH CANT COPY)

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Problem 89

In Problems 87–90, find the length s and the area A. Round answers to three decimal places.
(GRAPH CANT COPY)

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Problem 90

In Problems 87–90, find the length s and the area A. Round answers to three decimal places.
(GRAPH CANT COPY)

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Problem 91

The minute hand of a clock is 6 inches long. How far does the tip of the minute hand move in 15 minutes? How far does it move in 25 minutes? Round answers to two decimal places.
(IMAGE CANT COPY)

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Problem 92

Movement of a Pendulum 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.

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Problem 93

Area of a Sector Find the area of the sector of a circle of radius 4 meters formed by an angle of $45^{\circ} .$ Round the answer to two decimal places.

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Problem 94

Area of a Sector 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.

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Problem 95

Watering a Lawn A water sprinkler sprays water over a distance of 30 feet while rotating through an angle of $135^{\circ} .$ What area of lawn receives water?
(IMAGE CANT COPY)

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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?

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Problem 97

Windshield wiper The arm and blade of a windshield wiper have a total length of 34 inches. If the blade is 25 inches long and the wiper sweeps out an angle of $120^{\circ},$ how much window area can the blade clean?

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Problem 98

Windshield Wiper 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

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Problem 99

Motion on a Circle An object is traveling on a circle with a radius of 5 centimeters. If in 20 seconds a central angle of $\frac{1}{3}$ radian is swept out, what is the angular speed of the object? What is its linear speed?

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Problem 100

Motion on a Circle An object is traveling on a circle with a radius of 2 meters. If in 20 seconds the object travels
5 meters, what is its angular speed? What is its linear speed?

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Problem 101

A musement Park Ride A gondola on an amusement park ride, similar to the Spin Cycle at Silverwood Theme Park, spins at a speed of 13 revolutions per minute. If the gondola is 25 feet from the ride's center, what is the linear speed of the gondola in miles per hour?

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Problem 102

A musement Park Ride A centrifugal force ride, similar to the Gravitron, spins at a speed 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?

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Problem 103

Bla-ray Drive A Blu-ray drive has a maximum speed of $10,000$ revolutions per minute. If a Blu-ray disc has a diameter of $12 \mathrm{cm},$ what is the linear speed, in $\mathrm{km} / \mathrm{h}$, of a point $4 \mathrm{cm}$ from the center if the disc is spinning at a rate of 8000 revolutions per minute?

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Problem 104

A DVD drive has a maximum speed of 7200 revolutions per minute. If a DVD has a diameter of 12 cm, what is the linear speed, in km/h, of a point 5 cm from the disc’s center if it is spinning at a rate of 5400 revolutions per minute?

Katelyn Chen

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Problem 105

Bicycle Wheels The diameter of each wheel of a bicycle is 26 inches. If you are traveling at a speed of 35 miles per hour on this bicycle, through how many revolutions per minute are the wheels turning?
(IMAGE CANT COPY)

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Problem 106

Car Wheels 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.

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Problem 107

In Problems 107–110, 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.
Distance between Cities Memphis, Tennessee, is due north of New Orleans, Louisiana. Find the distance between Memphis $\left(35^{\circ} 9^{\circ} \text { north latitude) and New Orleans }\left(29^{\circ} 57^{\prime}\right.\right.$ north latitude). Assume that the radius of Earth is 3960 miles.
(GRAPH CANT COPY)

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Problem 108

In Problems 107–110, 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.
Distance between Cities Charleston, West Virginia, is due north of Jacksonville, Florida. Find the distance between Charleston $\left(38^{\circ} 21^{\prime \prime} \text { north latitude) and Jacksonville }\left(30^{\circ} 20^{\circ}\right.\right.$ north latitude). Assume that the radius of Earth is 3960 miles
(GRAPH CANT COPY)

Katelyn Chen

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Problem 109

In Problems 107–110, 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.
Linear Speed on Earth rotates on an axis through its poles The distance from the axis to a location on Earth at $30^{\circ}$ north latitude is about 3429.5 miles. Therefore, a location on Earth at $30^{\circ}$ north latitude is spinning on a circle of radius 3429.5 miles Compute the linear speed on the surface of Earth at $30^{\circ}$ north latitude.
(GRAPH CANT COPY)

Katelyn Chen

Numerade Educator

Problem 110

In Problems 107–110, 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.
Linear Speed on Farth 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.
(GRAPH CANT COPY)

Katelyn Chen

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Problem 111

Speed of the Moon The mean distance of the moon from Earth is $2.39 \times 10^{5}$ miles. A ssuming that the orbit of the moon around Earth is circular and that 1 revolution takes 27.3 days, find the linear speed of the moon. Express your answer in miles per hour.

Katelyn Chen

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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.

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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

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Problem 114

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

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Problem 115

To approximate the speed of the current of a river, a circular paddle wheel with radius 4 feet is lowered into the water. If the current causes the wheel to rotate at a speed of 10 revolutions per minute, what is the speed of the current? Express your answer in miles per hour.

Katelyn Chen

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Problem 116

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?

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Problem 117

At the Cable Car Museum you can see the four cable lines that are used to pull cable cars up and down the hills of San Francisco. Each cable travels at a speed of 9.55 miles per hour, driven by a rotating wheel whose diameter is 8.5 feet. How fast is the wheel rotating? Express your answer in revolutions per minute.

Katelyn Chen

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Problem 118

Naples, Florida, is about 90 miles due west of Ft. Lauderdale. How much sooner would a person in Ft. Lauderdale first see the rising Sun than a person in Naples? [Hint: Consult the figure. When a person at $Q$ sees the first rays of the Sun, a person at $P$ is still in the dark. The person at $P$ sees the first rays after Earth has rotated until $P$ is at the location $Q$. Now use the fact that at the latitude of Ft. Lauderdale, in 24 hours an arc of length $2 \pi(3559)$ miles is subtended.
(GRAPH CANT COPY)

Katelyn Chen

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Problem 119

$A$ dog is attached to a 9 -foot rope fastencd to the outside corner of a fenced-in garden that measures 6 feet by 10 feet. Assuming that the dog cannot enter the garden, compute the exact area the dog can wander. Write the exact area in square feet."

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Problem 120

The measure of arc $\overline{B E}$ 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 $A$."
(GRAPH CANT COPY)

Kratika Bhadauria

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Problem 121

How fast would you have to travel on the surface of Earth at the equator to keep up with the Sun (that is so that the Sun would appear to remain in the same position in the sky)?

Katelyn Chen

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Problem 122

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 (top, right). If the radius of Earth is taken as 3960 miles, express 1 nautical mile in terms of ordinary, or statute, miles.
(GRAPH CANT COPY)

Katelyn Chen

Numerade Educator

Problem 123

Eratosthenes of Cyrene $(276-195$ ac) 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 Soo 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.
(GRAPH CANT COPY)

Katelyn Chen

Numerade Educator

Problem 124

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.
[Note: There is a $90^{\circ}$ angle between the two foul lines. Then there are two $3^{\circ}$ angles between the foul lines and the dashed lines shown. The angle between the two dashed lines outside the $\left.200 \text { -foot foul lines is } 96^{\circ} .\right]$
(GRAPH CANT COPY)

Katelyn Chen

Numerade Educator

Problem 125

Pulleys 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
$$
\frac{r_{1}}{r_{2}}=\frac{\omega_{2}}{\omega_{1}}
$$

Katelyn Chen

Numerade Educator

Problem 126

Do you prefer to measure angles using degrees or radians? Provide justification and a rationale for your choice.

Katelyn Chen

Numerade Educator

Problem 127

What is 1 radian? What is 1 degree?

Katelyn Chen

Numerade Educator

Problem 128

Which angle has the larger measure: 1 degree or 1 radian? Or are they equal?

Katelyn Chen

Numerade Educator

Problem 129

Explain the difference between linear speed and angular speed.

Katelyn Chen

Numerade Educator

Problem 130

For a circle of radius $r,$ a central angle of $\theta$ degrees subtends an are whose length $s$ is $s=\frac{\pi}{180} r \theta .$ Discuss whether this statement is true or false. Defend your position.

Katelyn Chen

Numerade Educator

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

Numerade Educator

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

Numerade Educator

Problem 133

In Example $6,$ we found that the distance between Dallas. Texas, and Sioux Falls, South Dakota, is approximately 744 miles. According to mapquest.com, the distance is approximately 850 miles. What might account for the difference?

Katelyn Chen

Numerade Educator

Problem 134

Problems 134–137 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 the zero of $f(x)=3 x+7$

Katelyn Chen

Numerade Educator

Problem 135

Problems 134–137 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.
$$
\text { Solve: } 5 x^{2}+2=5-14 x
$$

Katelyn Chen

Numerade Educator

Problem 136

Problems 134–137 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.
Write the function that is finally graphed if all of the following transformations are applied to the graph of $y=|x|$
(a) Shift left 3 units. (b) Reflect about the $x$ -axis. (c) Shift down 4 units.

Katelyn Chen

Numerade Educator

Problem 137

Problems 134–137 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 the horizontal and vertical asymptotes of $R(x)=\frac{3 x^{2}-12}{x^{2}-5 x-14}$

Katelyn Chen

Numerade Educator