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Chapter 4

Trigonometry

Educators

WZ

Problem 1

________ means "measurement of triangles."

Heather Z.
Numerade Educator

Problem 2

An ________ is determined by rotating a ray about its endpoint.

Heather Z.
Numerade Educator

Problem 3

Two angles that have the same initial and terminal sides are ________.

Heather Z.
Numerade Educator

Problem 4

One ________ is the measure of a central angle that intercepts an arc equal to the radius of the circle.

Heather Z.
Numerade Educator

Problem 5

Angles that measure between $0$ and $\pi/2$ are ________ angles, and angles that measure between $\pi/2$ and $\pi$ are ________ angles.

Heather Z.
Numerade Educator

Problem 6

Two positive angles that have a sum of $\pi/2$ are ________ angles, whereas two positive angles that have a sum of $\pi$ are ________ angles.

Heather Z.
Numerade Educator

Problem 7

The angle measure that is equivalent to a rotation of $\frac{1}{360}$ of a complete revolution about an angle's vertex is one ________.

Heather Z.
Numerade Educator

Problem 8

180 degrees $=$ ________ radians.

Heather Z.
Numerade Educator

Problem 9

The ________ speed of a particle is the ratio of arc length to time traveled, and the ________ speed of a particle is the ratio of central angle to time traveled.

Heather Z.
Numerade Educator

Problem 10

The area $A$ of a sector of a circle with radius $r$ and central angle $\thata$, where $\thata$ is measured in radians, is given by the formula ________.

Heather Z.
Numerade Educator

Problem 11

In Exercises 11-16, estimate the angle to the nearest one-half radian.

Heather Z.
Numerade Educator

Problem 12

In Exercises 11-16, estimate the angle to the nearest one-half radian.

Heather Z.
Numerade Educator

Problem 13

In Exercises 11-16, estimate the angle to the nearest one-half radian.

Heather Z.
Numerade Educator

Problem 14

In Exercises 11-16, estimate the angle to the nearest one-half radian.

Heather Z.
Numerade Educator

Problem 15

In Exercises 11-16, estimate the angle to the nearest one-half radian.

Heather Z.
Numerade Educator

Problem 16

In Exercises 11-16, estimate the angle to the nearest one-half radian.

Heather Z.
Numerade Educator

Problem 17

In Exercises 17-22, determine the quadrant in which each angle lies. (The angle measure is given in radians.)

(a) $\frac{\pi}{4}$
(b) $\frac{5\pi}{4}$

Heather Z.
Numerade Educator

Problem 18

In Exercises 17-22, determine the quadrant in which each angle lies. (The angle measure is given in radians.)

(a) $\frac{11\pi}{8}$
(b) $\frac{9\pi}{8}$

Heather Z.
Numerade Educator

Problem 19

In Exercises 17-22, determine the quadrant in which each angle lies. (The angle measure is given in radians.)

(a) $-\frac{\pi}{6}$
(b) $-\frac{\pi}{3}$

Heather Z.
Numerade Educator

Problem 20

In Exercises 17-22, determine the quadrant in which each angle lies. (The angle measure is given in radians.)

(a) $-\frac{5\pi}{6}$
(b) $-\frac{11\pi}{9}$

Heather Z.
Numerade Educator

Problem 21

In Exercises 17-22, determine the quadrant in which each angle lies. (The angle measure is given in radians.)

(a) $3.5$
(b) $2.25$

Heather Z.
Numerade Educator

Problem 22

In Exercises 17-22, determine the quadrant in which each angle lies. (The angle measure is given in radians.)

(a) $6.02$
(b) $-4.25$

Heather Z.
Numerade Educator

Problem 23

In Exercises 23-26, sketch each angle in standard position.

(a) $\frac{\pi}{3}$
(b) $-\frac{2\pi}{3}$

Heather Z.
Numerade Educator

Problem 24

In Exercises 23-26, sketch each angle in standard position.

(a) $-\frac{7\pi}{4}$
(b) $\frac{5\pi}{2}$

Heather Z.
Numerade Educator

Problem 25

In Exercises 23-26, sketch each angle in standard position.

(a) $\frac{11\pi}{6}$
(b) $-3$

Heather Z.
Numerade Educator

Problem 26

In Exercises 23-26, sketch each angle in standard position.

(a) $4$
(b) $7\pi$

Heather Z.
Numerade Educator

Problem 27

In Exercises 27-30, determine two coterminal angles (one positive and one negative) for each angle. Give your answers in radians.

(a) $\theta = \frac{\pi}{6}$
(b) $\theta = \frac{5\pi}{6}$

Heather Z.
Numerade Educator

Problem 28

In Exercises 27-30, determine two coterminal angles (one positive and one negative) for each angle. Give your answers in radians.

(a) $\theta = \frac{7\pi}{6}$
(b) $\theta = -\frac{11\pi}{6}$

Heather Z.
Numerade Educator

Problem 29

In Exercises 27-30, determine two coterminal angles (one positive and one negative) for each angle. Give your answers in radians.

(a) $\theta = \frac{2\pi}{3}$
(b) $\theta = \frac{\pi}{12}$

Heather Z.
Numerade Educator

Problem 30

In Exercises 27-30, determine two coterminal angles (one positive and one negative) for each angle. Give your answers in radians.

(a) $\theta = -\frac{9\pi}{4}$
(b) $\theta = -\frac{2\pi}{15}$

Heather Z.
Numerade Educator

Problem 31

In Exercises 31-34, find (if possible) the complement and supplement of each angle.

(a) $\pi /3$
(b) $\pi /4$

Heather Z.
Numerade Educator

Problem 32

In Exercises 31-34, find (if possible) the complement and supplement of each angle.

(a) $\pi /12$
(b) $11\pi /12$

Heather Z.
Numerade Educator

Problem 33

In Exercises 31-34, find (if possible) the complement and supplement of each angle.

(a) $1$
(b) $2$

Heather Z.
Numerade Educator

Problem 34

In Exercises 31-34, find (if possible) the complement and supplement of each angle.

(a) $3$
(b) $1.5$

Heather Z.
Numerade Educator

Problem 35

In Exercises 35-40, estimate the number of degrees in the angle. Use a protractor to check your answer.

Heather Z.
Numerade Educator

Problem 36

In Exercises 35-40, estimate the number of degrees in the angle. Use a protractor to check your answer.

Heather Z.
Numerade Educator

Problem 37

In Exercises 35-40, estimate the number of degrees in the angle. Use a protractor to check your answer.

Heather Z.
Numerade Educator

Problem 38

In Exercises 35-40, estimate the number of degrees in the angle. Use a protractor to check your answer.

Heather Z.
Numerade Educator

Problem 39

In Exercises 35-40, estimate the number of degrees in the angle. Use a protractor to check your answer.

Heather Z.
Numerade Educator

Problem 40

In Exercises 35-40, estimate the number of degrees in the angle. Use a protractor to check your answer.

Heather Z.
Numerade Educator

Problem 41

In Exercises 41-44, determine the quadrant in which each angle lies.

(a) $130^{\circ}$

(b) $285^{\circ}$

Heather Z.
Numerade Educator

Problem 42

In Exercises 41-44, determine the quadrant in which each angle lies.

(a) $8.3^{\circ}$

(b) $257^{\circ} 30'$

Heather Z.
Numerade Educator

Problem 43

In Exercises 41-44, determine the quadrant in which each angle lies.

(a) $-132^{\circ} 50'$

(b) $-336^{\circ}$

Heather Z.
Numerade Educator

Problem 44

In Exercises 41-44, determine the quadrant in which each angle lies.

(a) $-260^{\circ}$

(b) $-3.4^{\circ}$

Heather Z.
Numerade Educator

Problem 45

In Exercises 45-48, sketch each angle in standard position.

(a) $90^{\circ}$

(b) $180^{\circ}$

Heather Z.
Numerade Educator

Problem 46

In Exercises 45-48, sketch each angle in standard position.

(a) $270^{\circ}$

(b) $120^{\circ}$

Heather Z.
Numerade Educator

Problem 47

In Exercises 45-48, sketch each angle in standard position.

(a) $-30^{\circ}$

(b) $-135^{\circ}$

Heather Z.
Numerade Educator

Problem 48

In Exercises 45-48, sketch each angle in standard position.

(a) $-750^{\circ}$

(b) $-600^{\circ}$

Heather Z.
Numerade Educator

Problem 49

In Exercises 49-52, determine two coterminal angles (one positive and one negative) for each angle. Give your answers in degrees.

(a) $\theta = 45^{\circ}$
(b) $\theta = -36^{\circ}$

Heather Z.
Numerade Educator

Problem 50

In Exercises 49-52, determine two coterminal angles (one positive and one negative) for each angle. Give your answers in degrees.

(a) $\theta = 120^{\circ}$
(b) $\theta = -420^{\circ}$

Heather Z.
Numerade Educator

Problem 51

In Exercises 49-52, determine two coterminal angles (one positive and one negative) for each angle. Give your answers in degrees.

(a) $\theta = 240^{\circ}$
(b) $\theta = -180^{\circ}$

Heather Z.
Numerade Educator

Problem 52

In Exercises 49-52, determine two coterminal angles (one positive and one negative) for each angle. Give your answers in degrees.

(a) $\theta = -390^{\circ}$
(b) $\theta = 230^{\circ}$

Heather Z.
Numerade Educator

Problem 53

In Exercises 53-56, find (if possible) the complement and supplement of each angle.

(a) $18^{\circ}$
(b) $85^{\circ}$

Heather Z.
Numerade Educator

Problem 54

In Exercises 53-56, find (if possible) the complement and supplement of each angle.

(a) $46^{\circ}$
(b) $93^{\circ}$

Heather Z.
Numerade Educator

Problem 55

In Exercises 53-56, find (if possible) the complement and supplement of each angle.

(a) $150^{\circ}$
(b) $79^{\circ}$

Heather Z.
Numerade Educator

Problem 56

In Exercises 53-56, find (if possible) the complement and supplement of each angle.

(a) $130^{\circ}$
(b) $170^{\circ}$

Heather Z.
Numerade Educator

Problem 57

In Exercises 57-60, rewrite each angle in radian measure as a multiple of $\pi$. (Do not use a calculator.)

(a) $30^{\circ}$
(b) $45^{\circ}$

Heather Z.
Numerade Educator

Problem 58

In Exercises 57-60, rewrite each angle in radian measure as a multiple of $\pi$. (Do not use a calculator.)

(a) $315^{\circ}$
(b) $120^{\circ}$

Heather Z.
Numerade Educator

Problem 59

In Exercises 57-60, rewrite each angle in radian measure as a multiple of $\pi$. (Do not use a calculator.)

(a) $-20^{\circ}$
(b) $-60^{\circ}$

Heather Z.
Numerade Educator

Problem 60

Rewrite each angle in radian measure as a multiple of $\pi$.
(a) $-270^{\circ}$
(b) $144^{\circ}$

Heather Z.
Numerade Educator

Problem 61

In Exercises 61-64, rewrite each angle in degree measure.(Do not use a calculator.)

(a) $\frac{3\pi}{2}$
(b) $\frac{7\pi}{2}$

Heather Z.
Numerade Educator

Problem 62

In Exercises 61-64, rewrite each angle in degree measure.(Do not use a calculator.)

(a) $-\frac{7\pi}{12}$
(b) $\frac{\pi}{9}$

Heather Z.
Numerade Educator

Problem 63

In Exercises 61-64, rewrite each angle in degree measure.(Do not use a calculator.)

(a) $\frac{5\pi}{4}$
(b) $-\frac{7\pi}{3}$

Heather Z.
Numerade Educator

Problem 64

In Exercises 61-64, rewrite each angle in degree measure.(Do not use a calculator.)

(a) $\frac{11\pi}{6}$
(b) $\frac{34\pi}{15}$

Heather Z.
Numerade Educator

Problem 65

In Exercises 65-72, convert the angle measure from degrees to radians. Round to three decimal places.

$45^{\circ}$

Heather Z.
Numerade Educator

Problem 66

In Exercises 65-72, convert the angle measure from degrees to radians. Round to three decimal places.

$87.4^{\circ}$

Heather Z.
Numerade Educator

Problem 67

In Exercises 65-72, convert the angle measure from degrees to radians. Round to three decimal places.

$-216.35^{\circ}$

Heather Z.
Numerade Educator

Problem 68

In Exercises 65-72, convert the angle measure from degrees to radians. Round to three decimal places.

$-48.27^{\circ}$

Heather Z.
Numerade Educator

Problem 69

In Exercises 65-72, convert the angle measure from degrees to radians. Round to three decimal places.

$532^{\circ}$

Heather Z.
Numerade Educator

Problem 70

In Exercises 65-72, convert the angle measure from degrees to radians. Round to three decimal places.

$345^{\circ}$

Heather Z.
Numerade Educator

Problem 71

In Exercises 65-72, convert the angle measure from degrees to radians. Round to three decimal places.

$-0.83^{\circ}$

Heather Z.
Numerade Educator

Problem 72

In Exercises 65-72, convert the angle measure from degrees to radians. Round to three decimal places.

$0.54^{\circ}$

Heather Z.
Numerade Educator

Problem 73

In Exercises 73-80, convert the angle measure from radians to degrees. Round to three decimal places.

$\pi/7$

Heather Z.
Numerade Educator

Problem 74

In Exercises 73-80, convert the angle measure from radians to degrees. Round to three decimal places.

$5\pi/11$

Heather Z.
Numerade Educator

Problem 75

In Exercises 73-80, convert the angle measure from radians to degrees. Round to three decimal places.

$15\pi/8$

Heather Z.
Numerade Educator

Problem 76

In Exercises 73-80, convert the angle measure from radians to degrees. Round to three decimal places.

$13\pi/2$

Heather Z.
Numerade Educator

Problem 77

In Exercises 73-80, convert the angle measure from radians to degrees. Round to three decimal places.

$-4.2\pi$

Heather Z.
Numerade Educator

Problem 78

convert the angle measure from radians to degrees. Round to three decimal places. $4.8 \pi$

Heather Z.
Numerade Educator

Problem 79

In Exercises 73-80, convert the angle measure from radians to degrees. Round to three decimal places.

$-2$

Heather Z.
Numerade Educator

Problem 80

In Exercises 73-80, convert the angle measure from radians to degrees. Round to three decimal places.

$-0.57$

Heather Z.
Numerade Educator

Problem 81

In Exercises 81-84, convert each angle measure to decimal degree form without using a calculator. Then check your answers using a calculator.

(a) $54^{\circ} 45'$

(b) $-128^{\circ} 30'$

Heather Z.
Numerade Educator

Problem 82

In Exercises 81-84, convert each angle measure to decimal degree form without using a calculator. Then check your answers using a calculator.

(a) $245^{\circ} 10'$

(b) $2^{\circ} 12'$

Heather Z.
Numerade Educator

Problem 83

In Exercises 81-84, convert each angle measure to decimal degree form without using a calculator. Then check your answers using a calculator.

(a) $85^{\circ} 18' 30''$

(b) $330^{\circ} 25''$

Heather Z.
Numerade Educator

Problem 84

In Exercises 81-84, convert each angle measure to decimal degree form without using a calculator. Then check your answers using a calculator.

(a) $-135^{\circ} 36''$

(b) $-408^{\circ} 16' 20''$

Heather Z.
Numerade Educator

Problem 85

In Exercises 85-88, convert each angle measure to degrees,minutes, and seconds without using a calculator. Then check your answers using a calculator.

(a) $240.6^{\circ}$

(b) $-145.8^{\circ}$

Heather Z.
Numerade Educator

Problem 86

In Exercises 85-88, convert each angle measure to degrees,minutes, and seconds without using a calculator. Then check your answers using a calculator.

(a) $-345.12^{\circ}$

(b) $0.45^{\circ}$

Heather Z.
Numerade Educator

Problem 87

In Exercises 85-88, convert each angle measure to degrees,minutes, and seconds without using a calculator. Then check your answers using a calculator.

(a) $2.5^{\circ}$

(b) $-3.58^{\circ}$

Heather Z.
Numerade Educator

Problem 88

In Exercises 85-88, convert each angle measure to degrees,minutes, and seconds without using a calculator. Then check your answers using a calculator.

(a) $-0.36^{\circ}$

(b) $0.79^{\circ}$

Heather Z.
Numerade Educator

Problem 89

In Exercises 89-92, find the length of the arc on a circle of radius $r$ intercepted by a central angle $theta$.

$Radius$ $r$
15 inches

$Central$ $Angle$ $\theta$
$120^{\circ}$

Heather Z.
Numerade Educator

Problem 90

In Exercises 89-92, find the length of the arc on a circle of radius $r$ intercepted by a central angle $theta$.

$Radius$ $r$
9 feet

$Central$ $Angle$ $\theta$
$60^{\circ}$

Heather Z.
Numerade Educator

Problem 91

In Exercises 89-92, find the length of the arc on a circle of radius $r$ intercepted by a central angle $theta$.

$Radius$ $r$
3 meter

$Central$ $Angle$ $\theta$
$150^{\circ}$

Heather Z.
Numerade Educator

Problem 92

In Exercises 89-92, find the length of the arc on a circle of radius $r$ intercepted by a central angle $theta$.

$Radius$ $r$
20 centimeters

$Central$ $Angle$ $\theta$
$45^{\circ}$

Heather Z.
Numerade Educator

Problem 93

In Exercises 93-96, find the radian measure of the central angle of a circle of radius $r$ that intercepts an arc of length $s$.

$Radius$ $r$
4 inches

$Arc$ $Length$ $s$
18 inches

Heather Z.
Numerade Educator

Problem 94

In Exercises 93-96, find the radian measure of the central angle of a circle of radius $r$ that intercepts an arc of length $s$.

$Radius$ $r$
14 feet

$Arc$ $Length$ $s$
8 feet

Heather Z.
Numerade Educator

Problem 95

In Exercises 93-96, find the radian measure of the central angle of a circle of radius $r$ that intercepts an arc of length $s$.

$Radius$ $r$
25 centimeters

$Arc$ $Length$ $s$
10.5 centimeters

Heather Z.
Numerade Educator

Problem 96

In Exercises 93-96, find the radian measure of the central angle of a circle of radius $r$ that intercepts an arc of length $s$.

$Radius$ $r$
80 kilometers

$Arc$ $Length$ $s$
150 kilometers

Heather Z.
Numerade Educator

Problem 97

In Exercises 97-100, use the given arc length and radius to find the angle $\theta$ (in radians).

Heather Z.
Numerade Educator

Problem 98

In Exercises 97-100, use the given arc length and radius to find the angle $\theta$ (in radians).

Heather Z.
Numerade Educator

Problem 99

In Exercises 97-100, use the given arc length and radius to find the angle $\theta$ (in radians).

Heather Z.
Numerade Educator

Problem 100

In Exercises 97-100, use the given arc length and radius to find the angle $\theta$ (in radians).

Heather Z.
Numerade Educator

Problem 101

In Exercises 101-104, find the area of the sector of the circle with radius $r$ and central angle $\theta$.

$Radius$ $r$
6 inches

$Central$ $Angle$ $\theta$
$\pi/3$

Heather Z.
Numerade Educator

Problem 102

In Exercises 101-104, find the area of the sector of the circle with radius $r$ and central angle $\theta$.

$Radius$ $r$
12 millimeters

$Central$ $Angle$ $\theta$
$\pi/4$

Heather Z.
Numerade Educator

Problem 103

In Exercises 101-104, find the area of the sector of the circle with radius $r$ and central angle $\theta$.

$Radius$ $r$
2.5 feet

$Central$ $Angle$ $\theta$
225$^\circ$

Heather Z.
Numerade Educator

Problem 104

In Exercises 101-104, find the area of the sector of the circle with radius $r$ and central angle $\theta$.

$Radius$ $r$
1.4 miles

$Central$ $Angle$ $\theta$
330$^\circ$

Heather Z.
Numerade Educator

Problem 105

DISTANCE BETWEEN CITIES In Exercises 105 and 106, find the distance between the cities. Assume that Earth is a sphere of radius 4000 miles and that the cities are on the same longitude (one city is due north of the other).

$City$
Dallas, Texas

$Latitude$
$32^{\circ} 47' 39'' N$

$City$
Omaha, Nebraska

$Latitude$
$41^{\circ} 15' 50'' N$

Heather Z.
Numerade Educator

Problem 106

DISTANCE BETWEEN CITIES In Exercises 105 and 106, find the distance between the cities. Assume that Earth is a sphere of radius 4000 miles and that the cities are on the same longitude (one city is due north of the other).

$City$
San Francisco, California

$Latitude$
$37^{\circ} 47' 36'' N$

$City$
Seattle, Washington

$Latitude$
$47^{\circ} 37' 18'' N$

Heather Z.
Numerade Educator

Problem 107

DIFFERENCE IN LATITUDES Assuming that Earth is a sphere of radius 6378 kilometers, what is the difference in the latitudes of Syracuse, New York and Annapolis, Maryland, where Syracuse is about 450 kilometers due north of Annapolis?

Heather Z.
Numerade Educator

Problem 108

DIFFERENCE IN LATITUDES Assuming that Earth is a sphere of radius 6378 kilometers, what is the difference in the latitudes of Lynchburg, Virginia and Myrtle Beach, South Carolina, where Lynchburg is about 400 kilometers due north of Myrtle Beach?

Heather Z.
Numerade Educator

Problem 109

INSTRUMENTATION The pointer on a voltmeter is 6 centimeters in length (see figure). Find the angle through which the pointer rotates when it moves 2.5 centimeters on the scale.

Heather Z.
Numerade Educator

Problem 110

ELECTRIC HOIST An electric hoist is being used to lift a beam (see figure). The diameter of the drum on the hoist is 10 inches, and the beam must be raised 2 feet. Find the number of degrees through which the drum must rotate.

Heather Z.
Numerade Educator

Problem 111

LINEAR AND ANGULAR SPEEDS A circular power saw has a $7\frac{1}{4}$-inch-diameter blade that rotates at 5000 revolutions per minute.

(a) Find the angular speed of the saw blade in radians per minute.

(b) Find the linear speed (in feet per minute) of one of the 24 cutting teeth as they contact the wood being cut.

Heather Z.
Numerade Educator

Problem 112

LINEAR AND ANGULAR SPEEDS A carousel with a 50-foot diameter makes 4 revolutions per minute.

(a) Find the angular speed of the carousel in radians per minute.
(b) Find the linear speed (in feet per minute) of the platform rim of the carousel.

Heather Z.
Numerade Educator

Problem 113

LINEAR AND ANGULAR SPEEDS The diameter of a DVD is approximately 12 centimeters. The drive motor of the DVD player is controlled to rotate precisely between 200 and 500 revolutions per minute, depending on what track is being read.

(a) Find an interval for the angular speed of a DVD as it rotates.

(b) Find an interval for the linear speed of a point on the outermost track as the DVD rotates.

Heather Z.
Numerade Educator

Problem 114

ANGULAR SPEED A two-inch-diameter pulley on an electric motor that runs at 1700 revolutions per minute is connected by a belt to a four-inch-diameter pulley on a saw arbor.

(a) Find the angular speed (in radians per minute) of each pulley.
(b) Find the revolutions per minute of the saw.

Heather Z.
Numerade Educator

Problem 115

ANGULAR SPEED A car is moving at a rate of 65 miles per hour, and the diameter of its wheels is 2 feet.

(a) Find the number of revolutions per minute the wheels are rotating.
(b) Find the angular speed of the wheels in radians per minute.

Heather Z.
Numerade Educator

Problem 116

ANGULAR SPEED A computerized spin balance machine rotates a 25-inch-diameter tire at 480 revolutions per minute.

(a) Find the road speed (in miles per hour) at which the tire is being balanced.
(b) At what rate should the spin balance machine be set so that the tire is being tested for 55 miles per hour?

Heather Z.
Numerade Educator

Problem 117

AREA A sprinkler on a golf green is set to spray water over a distance of 15 meters and to rotate through an angle of $140^{\circ}$. Draw a diagram that shows the region that can be irrigated with the sprinkler. Find the area of the region.

Heather Z.
Numerade Educator

Problem 118

AREA A car's rear windshield wiper rotates $125^{\circ}$. The total length of the wiper mechanism is 25 inches and wipes the windshield over a distance of 14 inches.Find the area covered by the wiper.

Heather Z.
Numerade Educator

Problem 119

SPEED OF A BICYCLE The radii of the pedal sprocket, the wheel sprocket, and the wheel of the bicycle in the figure are 4 inches, 2 inches, and 14 inches, respectively. A cyclist is pedaling at a rate of 1 revolution per second.

(a) Find the speed of the bicycle in feet per second and miles per hour.

(b) Use your result from part (a) to write a function for the distance $d$ (in miles) a cyclist travels in terms of the number $n$ of revolutions of the pedal sprocket.

(c) Write a function for the distance $d$ (in miles) a cyclist travels in terms of the time $t$ (in seconds). Compare this function with the $t$ function from part (b).

(d) Classify the types of functions you found in parts(b) and (c). Explain your reasoning.

Heather Z.
Numerade Educator

Problem 120

CAPSTONE Write a short paper in your own words explaining the meaning of each of the following concepts to a classmate.

(a) an angle in standard position
(b) positive and negative angles
(c) coterminal angles
(d) angle measure in degrees and radians
(e) obtuse and acute angles
(f ) complementary and supplementary angles

Heather Z.
Numerade Educator

Problem 121

TRUE OR FALSE? In Exercises 121-123, determine whether the statement is true or false. Justify your answer.

A measurement of 4 radians corresponds to two complete revolutions from the initial side to the terminal side of an angle.

Heather Z.
Numerade Educator

Problem 122

TRUE OR FALSE? In Exercises 121-123, determine whether the statement is true or false. Justify your answer.

The difference between the measures of two coterminal angles is always a multiple of $360^{\circ}$ if expressed in degrees and is always a multiple of $2\pi$ radians if expressed in radians.

Heather Z.
Numerade Educator

Problem 123

TRUE OR FALSE? In Exercises 121-123, determine whether the statement is true or false. Justify your answer.

An angle that measures $ - 1260^{\circ}$ lies in Quadrant III.

Heather Z.
Numerade Educator

Problem 124

THINK ABOUT IT A fan motor turns at a given angular speed. How does the speed of the tips of the blades change if a fan of greater diameter is installed on the motor? Explain.

Heather Z.
Numerade Educator

Problem 125

THINK ABOUT IT Is a degree or a radian the larger unit of measure? Explain.

Heather Z.
Numerade Educator

Problem 126

WRITING If the radius of a circle is increasing and the magnitude of a central angle is held constant, how is the length of the intercepted arc changing? Explain your reasoning.

Heather Z.
Numerade Educator

Problem 127

PROOF Prove that the area of a circular sector of radius $r$ with central angle $\theta$ is $A = \frac{1}{2}\theta r^2$, where $\theta$ is measured in radians.

Heather Z.
Numerade Educator