• Home
  • Textbooks
  • Essentials of Precalculus
  • Trigonometric Functions

Essentials of Precalculus

Richard N. Aufmann, Richard D. Nation

Chapter 4

Trigonometric Functions - all with Video Answers

Educators

+ 4 more educators

Section 1

Angles and Arcs

01:35

Problem 1

In Exercises 1 to $12,$ find the measure (if possible) of the complement and the supplement of each angle.
$$15^{\circ}$$

Chris Wojturski
Chris Wojturski
Numerade Educator
01:32

Problem 2

In Exercises 1 to $12,$ find the measure (if possible) of the complement and the supplement of each angle.
$$87^{\circ}$$

Vysakh M
Vysakh M
Numerade Educator
02:37

Problem 3

In Exercises 1 to $12,$ find the measure (if possible) of the complement and the supplement of each angle.
$$70^{\circ} 15^{\prime}$$

Chris Wojturski
Chris Wojturski
Numerade Educator
03:02

Problem 4

In Exercises 1 to $12,$ find the measure (if possible) of the complement and the supplement of each angle.
$$22^{\circ} 43^{\prime}$$

Chris Wojturski
Chris Wojturski
Numerade Educator
03:52

Problem 5

In Exercises 1 to $12,$ find the measure (if possible) of the complement and the supplement of each angle.
$$56^{6} 33^{\prime} 15^{\prime \prime}$$

Chris Wojturski
Chris Wojturski
Numerade Educator
03:25

Problem 6

In Exercises 1 to $12,$ find the measure (if possible) of the complement and the supplement of each angle.
$$19^{\circ} 42^{\prime} 05^{\prime \prime}$$

Chris Wojturski
Chris Wojturski
Numerade Educator
03:01

Problem 7

In Exercises 1 to $12,$ find the measure (if possible) of the complement and the supplement of each angle.
$$1$$

Chris Wojturski
Chris Wojturski
Numerade Educator
04:05

Problem 8

In Exercises 1 to $12,$ find the measure (if possible) of the complement and the supplement of each angle.
$$0.5$$

Chris Wojturski
Chris Wojturski
Numerade Educator
02:24

Problem 9

In Exercises 1 to $12,$ find the measure (if possible) of the complement and the supplement of each angle.
$$\frac{\pi}{4}$$

Chris Wojturski
Chris Wojturski
Numerade Educator
02:28

Problem 10

In Exercises 1 to $12,$ find the measure (if possible) of the complement and the supplement of each angle.
$$\frac{\pi}{3}$$

Chris Wojturski
Chris Wojturski
Numerade Educator
02:50

Problem 11

In Exercises 1 to $12,$ find the measure (if possible) of the complement and the supplement of each angle.
$$\frac{2 \pi}{5}$$

Chris Wojturski
Chris Wojturski
Numerade Educator
02:43

Problem 12

In Exercises 1 to $12,$ find the measure (if possible) of the complement and the supplement of each angle.
$$\frac{\pi}{6}$$

Chris Wojturski
Chris Wojturski
Numerade Educator
03:08

Problem 13

In Exercises 13 to $18,$ classify each angle by quadrant, and state the measure of the positive angle with measure less than $360^{\circ}$ that is coterminal with the given angle.
$$\alpha=610^{\circ}$$

Chris Wojturski
Chris Wojturski
Numerade Educator
02:02

Problem 14

In Exercises 13 to $18,$ classify each angle by quadrant, and state the measure of the positive angle with measure less than $360^{\circ}$ that is coterminal with the given angle.
$$\alpha=765^{\circ}$$

Chris Wojturski
Chris Wojturski
Numerade Educator
03:17

Problem 15

In Exercises 13 to $18,$ classify each angle by quadrant, and state the measure of the positive angle with measure less than $360^{\circ}$ that is coterminal with the given angle.
$$\alpha=-975^{\circ}$$

Chris Wojturski
Chris Wojturski
Numerade Educator
03:38

Problem 16

In Exercises 13 to $18,$ classify each angle by quadrant, and state the measure of the positive angle with measure less than $360^{\circ}$ that is coterminal with the given angle.
$$\alpha=-872^{\circ}$$

Chris Wojturski
Chris Wojturski
Numerade Educator
04:38

Problem 17

In Exercises 13 to $18,$ classify each angle by quadrant, and state the measure of the positive angle with measure less than $360^{\circ}$ that is coterminal with the given angle.
$$\alpha=2456^{\circ}$$

Chris Wojturski
Chris Wojturski
Numerade Educator
03:38

Problem 18

In Exercises 13 to $18,$ classify each angle by quadrant, and state the measure of the positive angle with measure less than $360^{\circ}$ that is coterminal with the given angle.
$$\alpha=-3789^{\circ}$$

Chris Wojturski
Chris Wojturski
Numerade Educator
03:00

Problem 19

In Exercises 19 to $24,$ use a calculator to convert each decimal degree measure to its equivalent DMS measure.
$$24.56^{\circ}$$

Chris Wojturski
Chris Wojturski
Numerade Educator
03:08

Problem 20

In Exercises 19 to $24,$ use a calculator to convert each decimal degree measure to its equivalent DMS measure.
$$110.24^{\circ}$$

Chris Wojturski
Chris Wojturski
Numerade Educator
03:59

Problem 21

In Exercises 19 to $24,$ use a calculator to convert each decimal degree measure to its equivalent DMS measure.
$$64.158^{\circ}$$

Chris Wojturski
Chris Wojturski
Numerade Educator
03:15

Problem 22

In Exercises 19 to $24,$ use a calculator to convert each decimal degree measure to its equivalent DMS measure.
$$18.96^{\circ}$$

Chris Wojturski
Chris Wojturski
Numerade Educator
03:38

Problem 23

In Exercises 19 to $24,$ use a calculator to convert each decimal degree measure to its equivalent DMS measure.
$$3.402^{\circ}$$

Chris Wojturski
Chris Wojturski
Numerade Educator
03:30

Problem 24

In Exercises 19 to $24,$ use a calculator to convert each decimal degree measure to its equivalent DMS measure.
$$224.282^{\circ}$$

Chris Wojturski
Chris Wojturski
Numerade Educator
02:52

Problem 25

In Exercises 25 to $30,$ use a calculator to convert each DMS measure to its equivalent decimal degree measure.
$$25^{\circ} 25^{\prime} 12^{\prime \prime}$$

Chris Wojturski
Chris Wojturski
Numerade Educator
02:41

Problem 26

In Exercises 25 to $30,$ use a calculator to convert each DMS measure to its equivalent decimal degree measure.
$$63^{\circ} 29^{\prime} 42^{\prime \prime}$$

Chris Wojturski
Chris Wojturski
Numerade Educator
02:32

Problem 27

In Exercises 25 to $30,$ use a calculator to convert each DMS measure to its equivalent decimal degree measure.
$$183^{\circ} 33^{\prime} 36^{\prime \prime}$$

Chris Wojturski
Chris Wojturski
Numerade Educator
02:49

Problem 28

In Exercises 25 to $30,$ use a calculator to convert each DMS measure to its equivalent decimal degree measure.
$$141^{\circ} 6^{\prime} 9^{\prime \prime}$$

Chris Wojturski
Chris Wojturski
Numerade Educator
02:46

Problem 29

In Exercises 25 to $30,$ use a calculator to convert each DMS measure to its equivalent decimal degree measure.
$$211^{\circ} 46^{\prime} 48^{\prime \prime}$$

Chris Wojturski
Chris Wojturski
Numerade Educator
02:59

Problem 30

In Exercises 25 to $30,$ use a calculator to convert each DMS measure to its equivalent decimal degree measure.
$$19^{\circ} 12^{\prime} 18^{\prime \prime}$$

Chris Wojturski
Chris Wojturski
Numerade Educator
01:56

Problem 31

In Exercises 31 to $39,$ convert the degree measure to exact radian measure.
$$30^{\circ}$$

Chris Wojturski
Chris Wojturski
Numerade Educator
03:08

Problem 32

In Exercises 31 to $39,$ convert the degree measure to exact radian measure.
$$-45^{\circ}$$

Chris Wojturski
Chris Wojturski
Numerade Educator
01:48

Problem 33

In Exercises 31 to $39,$ convert the degree measure to exact radian measure.
$$90^{\circ}$$

Chris Wojturski
Chris Wojturski
Numerade Educator
02:56

Problem 34

In Exercises 31 to $39,$ convert the degree measure to exact radian measure.
$$15^{\circ}$$

Chris Wojturski
Chris Wojturski
Numerade Educator
02:35

Problem 35

In Exercises 31 to $39,$ convert the degree measure to exact radian measure.
$$165^{\circ}$$

Chris Wojturski
Chris Wojturski
Numerade Educator
02:45

Problem 36

In Exercises 31 to $39,$ convert the degree measure to exact radian measure.
$$315^{\circ}$$

Chris Wojturski
Chris Wojturski
Numerade Educator
02:57

Problem 37

In Exercises 31 to $39,$ convert the degree measure to exact radian measure.
$$420^{\circ}$$

Chris Wojturski
Chris Wojturski
Numerade Educator
02:50

Problem 38

In Exercises 31 to $39,$ convert the degree measure to exact radian measure.
$$630^{\c39. $\frac{13 \pi}{4}$
41. $36^{\circ}$
43. $30^{\circ}$
$45.67 .5^{\circ}$
47. $660^{\circ}$
$\begin{array}{ll}\text { 49. } 85.94^{\circ} & \text { 5 I. } 2.32\end{array}$irc}$$

Chris Wojturski
Chris Wojturski
Numerade Educator
02:56

Problem 39

In Exercises 31 to $39,$ convert the degree measure to exact radian measure.
$$585^{\circ}$$

Chris Wojturski
Chris Wojturski
Numerade Educator
01:44

Problem 40

In Exercises 40 to $48,$ convert the radian measure to exact degree measure.
$$\frac{\pi}{4}$$

Chris Wojturski
Chris Wojturski
Numerade Educator
01:30

Problem 41

In Exercises 40 to $48,$ convert the radian measure to exact degree measure.
$$\frac{\pi}{5}$$

Chris Wojturski
Chris Wojturski
Numerade Educator
01:50

Problem 42

In Exercises 40 to $48,$ convert the radian measure to exact degree measure.
$$-\frac{2 \pi}{3}$$

Chris Wojturski
Chris Wojturski
Numerade Educator
01:30

Problem 43

In Exercises 40 to $48,$ convert the radian measure to exact degree measure.
$$\frac{\pi}{6}$$

Chris Wojturski
Chris Wojturski
Numerade Educator
01:28

Problem 44

In Exercises 40 to $48,$ convert the radian measure to exact degree measure.
$$\frac{\pi}{9}$$

Chris Wojturski
Chris Wojturski
Numerade Educator
01:35

Problem 45

In Exercises 40 to $48,$ convert the radian measure to exact degree measure.
$$\frac{3 \pi}{8}$$

Chris Wojturski
Chris Wojturski
Numerade Educator
01:57

Problem 46

In Exercises 40 to $48,$ convert the radian measure to exact degree measure.
$$\frac{11 \pi}{18}$$

Chris Wojturski
Chris Wojturski
Numerade Educator
01:58

Problem 47

In Exercises 40 to $48,$ convert the radian measure to exact degree measure.
$$\frac{11 \pi}{3}$$

Chris Wojturski
Chris Wojturski
Numerade Educator
01:44

Problem 48

In Exercises 40 to $48,$ convert the radian measure to exact degree measure.
$$\frac{6 \pi}{5}$$

Chris Wojturski
Chris Wojturski
Numerade Educator
02:08

Problem 49

In Exercises 49 to $54,$ convert radians to degrees or degrees to radians. Round answers to the nearest hundredth.
$$1.5$$

Chris Wojturski
Chris Wojturski
Numerade Educator
02:42

Problem 50

In Exercises 49 to $54,$ convert radians to degrees or degrees to radians. Round answers to the nearest hundredth.
$$-2.3$$

Chris Wojturski
Chris Wojturski
Numerade Educator
02:28

Problem 51

In Exercises 49 to $54,$ convert radians to degrees or degrees to radians. Round answers to the nearest hundredth.
$$133^{\circ}$$

Chris Wojturski
Chris Wojturski
Numerade Educator
02:50

Problem 52

In Exercises 49 to $54,$ convert radians to degrees or degrees to radians. Round answers to the nearest hundredth.
$$427^{\circ}$$

Chris Wojturski
Chris Wojturski
Numerade Educator
02:30

Problem 53

In Exercises 49 to $54,$ convert radians to degrees or degrees to radians. Round answers to the nearest hundredth.
$$8.25$$

Chris Wojturski
Chris Wojturski
Numerade Educator
02:32

Problem 54

In Exercises 49 to $54,$ convert radians to degrees or degrees to radians. Round answers to the nearest hundredth.
$$-90^{\circ}$$

Chris Wojturski
Chris Wojturski
Numerade Educator
00:43

Problem 55

In Exercises 55 to $58,$ find the measure in radians and degrees of the central angle of a circle subtended by the given arc. Round answers to the nearest hundredth.
$r=2$ inches, $s=8$ inches

Erika Bustos
Erika Bustos
Numerade Educator
00:51

Problem 56

In Exercises 55 to $58,$ find the measure in radians and degrees of the central angle of a circle subtended by the given arc. Round answers to the nearest hundredth.
$r=7$ feet, $s=4$ feet

Erika Bustos
Erika Bustos
Numerade Educator
00:57

Problem 57

In Exercises 55 to $58,$ find the measure in radians and degrees of the central angle of a circle subtended by the given arc. Round answers to the nearest hundredth.
$r=5.2$ centimeters, $s=12.4$ centimeters

Erika Bustos
Erika Bustos
Numerade Educator
00:55

Problem 58

In Exercises 55 to $58,$ find the measure in radians and degrees of the central angle of a circle subtended by the given arc. Round answers to the nearest hundredth.
$r=35.8$ meters, $s=84.3$ meters

Erika Bustos
Erika Bustos
Numerade Educator
00:35

Problem 59

In Exercises 59 to $62,$ find the measure of the intercepted arc of a circle with the given radius and central angle. Round answers to the nearest hundredth.
$$r=8 \text { inches, } \theta=\frac{\pi}{4}$$

Erika Bustos
Erika Bustos
Numerade Educator
00:42

Problem 60

In Exercises 59 to $62,$ find the measure of the intercepted arc of a circle with the given radius and central angle. Round answers to the nearest hundredth.
$$r=3 \text { feet, } \theta=\frac{7 \pi}{2}$$

Erika Bustos
Erika Bustos
Numerade Educator
00:50

Problem 61

In Exercises 59 to $62,$ find the measure of the intercepted arc of a circle with the given radius and central angle. Round answers to the nearest hundredth.
$$r=25 \text { centimeters, } \theta=42^{\circ}$$

Erika Bustos
Erika Bustos
Numerade Educator
00:45

Problem 62

In Exercises 59 to $62,$ find the measure of the intercepted arc of a circle with the given radius and central angle. Round answers to the nearest hundredth.
$$r=5 \text { meters, } \theta=144^{\circ}$$

Erika Bustos
Erika Bustos
Numerade Educator
00:26

Problem 63

Find the number of radians in $1 \frac{1}{2}$ revolutions.

Erika Bustos
Erika Bustos
Numerade Educator
00:30

Problem 64

Find the number of radians in $\frac{3}{8}$ revolution.

Erika Bustos
Erika Bustos
Numerade Educator
02:13

Problem 65

A pulley with a radius of 14 inches uses a belt to drive a pulley with a radius of 28 inches. The 14 -inch pulley turns through an angle of $150^{\circ} .$ Find the angle through which the 28 -inch pulley turns.

Khushbu Rani
Khushbu Rani
Numerade Educator
02:49

Problem 66

A pulley with a diameter of 1.2 meters uses a belt to drive a pulley with a diameter of 0.8 meter. The 1.2 -meter pulley turns through an angle of $240^{\circ} .$ Find the angle through which the 0.8 -meter pulley turns.

Oluwadamilola Ameobi
Oluwadamilola Ameobi
Numerade Educator
00:56

Problem 67

Find the angular speed, in radians per second, of the second hand on a clock.

Umar Sohail Qureshi
Umar Sohail Qureshi
Numerade Educator
01:36

Problem 68

Find the angular speed, in radians per second, of a point on the equator of the earth.

Umar Sohail Qureshi
Umar Sohail Qureshi
Numerade Educator
02:24

Problem 69

A wheel is rotating at 50 revolutions per minute. Find the angular speed in radians per second.

Bobby Barnes
Bobby Barnes
University of North Texas
01:08

Problem 70

A wheel is rotating at 200 revolutions per minute. Find the angular speed in radians per second.

Erika Bustos
Erika Bustos
Numerade Educator
01:46

Problem 71

The turntable of a record player turns at $33 \frac{1}{3}$ revolutions per minute. Find the angular speed in radians per second.

Erika Bustos
Erika Bustos
Numerade Educator
01:33

Problem 72

A car with a wheel of radius 14 inches is moving with a speed of 55 mph. Find the angular speed of the wheel in radians per second.

Umar Sohail Qureshi
Umar Sohail Qureshi
Numerade Educator
03:11

Problem 73

Each tire on a car has a radius of 15 inches. The tires are rotating at 450 revolutions per minute. Find the speed of the automobile to the nearest mile per hour.

Sheryl Ezze
Sheryl Ezze
Numerade Educator
01:53

Problem 74

Each tire on a truck has a radius of 18 inches. The tires are rotating at 500 revolutions per minute. Find the speed of the truck to the nearest mile per hour.

Umar Sohail Qureshi
Umar Sohail Qureshi
Numerade Educator
03:04

Problem 75

The chain wheel of Emma's bicycle has a radius of 3.5 inches. The rear gear has a radius of 1.75 inches, and the back tire has a radius of 12 inches. If Emma pedals for 150 revolutions of the chain wheel, how far will she travel? Round to the nearest foot.
(IMAGE CAN'T COPY).

Harmender Singh Yadav
Harmender Singh Yadav
Numerade Educator
02:13

Problem 76

A winch with a 6 -inch radius is used to lift a container. The winch is designed so that as it is rotated, the cable stays in contact with the surface of the winch. That is, the cable does not wrap on top of itself.
(IMAGE CAN'T COPY).
a. Find the distance the container is lifted as the winch is rotated through an angle of $\frac{5 \pi}{6}$ radians
b. Determine the angle, in radians, through which the winch must be rotated to lift the container a distance of 2 feet.

Umar Sohail Qureshi
Umar Sohail Qureshi
Numerade Educator
02:26

Problem 77

During the time the Concorde was flying, it could fly from London to New York City, a distance of 3460 miles, in 2 hours and 59 minutes.
(IMAGE CAN'T COPY).
a. What was the average linear speed of the Concorde in miles per hour during one of these flights? Round to the nearest mile per hour.
b. What was the average angular speed of the Concorde in radians per hour during one of these flights? Assume that the Concorde maintains an altitude of 10 miles and that the radius of Earth is 3960 miles. Round to the nearest hundredth of a radian per hour. 0.29 radian per hour
c. If the Concorde left London at 1 P.M., what time would it be expected to arrive in New York City? (Hint: New York City is five time zones to the west of London.) $10: 59 \mathrm{A} . \mathrm{M}$

AG
Ankit Gupta
Numerade Educator
02:23

Problem 78

A pilot is flying a supersonic jet plane from east to west along a path over the equator. How fast, in miles per hour, does the pilot need to fly to keep the sun in the same relative position to the airplane? Assume that the plane is flying at an altitude of 2 miles above Earth and that Earth has a radius of 3960 miles. Round to the nearest mile per hour. $1037 \mathrm{mph}$

Umar Sohail Qureshi
Umar Sohail Qureshi
Numerade Educator
02:06

Problem 79

At a time when the earth was 93,000,000 miles from the sun, you observed through a tinted glass that the diameter of the sun occupied an arc of $31^{\prime} .$ Determine, to the nearest ten thousand miles, the diameter of the sun.
(IMAGE CAN'T COPY).
(Hint: Because the radius of arc $A B$ is large and its central angle is small, the length of the diameter of the sun is approximately the length of the arc $A B .$ ) $840,000 \mathrm{mi}$

Umar Sohail Qureshi
Umar Sohail Qureshi
Numerade Educator
02:36

Problem 80

The minute hand on the clock atop city hall measures 6 feet 3 inches from its tip to its axle.
a. Through what angle (in radians) does the minute hand pass between 9: 12 A.M. and 9: 48 A.M.? $\frac{6 \pi}{5}$ radians
b. What distance, to the nearest tenth of a foot, does the tip of the minute hand travel during this period? $23.6 \mathrm{ft}$

Umar Sohail Qureshi
Umar Sohail Qureshi
Numerade Educator
03:23

Problem 81

On April 25 $1990,$ the Hubble Space Telescope (HST) was deployed into a circular orbit 625 kilometers above the surface of the earth. The HST completes an earth orbit every 1.61 hours.
(IMAGE CAN'T COPY).
a. Find the angular velocity, with respect to the center of the earth, of the HST. Round your answer to the nearest 0.1 radian per hour. 3.9 radians per hour
b. Find the linear velocity of the HST. (Hint: The radius of the earth is about 6370 kilometers.) Round your answer to the nearest 100 kilometers per hour. $27,300 \mathrm{km} / \mathrm{h}$

Sheryl Ezze
Sheryl Ezze
Numerade Educator
03:41

Problem 82

Eratosthenes, the fifth librarian of Alexandria ( 230 B.C.), was able to estimate the radius of the earth from the following data: The distance between the Egyptian cities of Alexandria and Syrene was 5000 stadia ( 520 miles). Syrene was located directly south of Alexandria. One summer, at noon, the sun was directly overhead at Syrene, whereas at the same time in Alexandria, the sun was at a $7.5^{\circ}$ angle from the zenith.
(IMAGE CAN'T COPY).
Eratosthenes reasoned that because the sun is far away, the rays of sunlight that reach the earth must be nearly parallel. From this assumption he concluded that the measure of $\angle A O S$ in the accompanying figure must be $7.5^{\circ} .$ Use this information to estimate the radius (to the nearest 10 miles) of the earth. $3970 \mathrm{mi}$

Nicole C
Nicole C
Numerade Educator
02:19

Problem 83

Assume that the bicycle in the figure is moving forward at a constant rate. Point $A$ is on the edge of the 30 -inch rear tire, and point $B$ is on the edge of the 20 -inch front tire.
(IMAGE CAN'T COPY).
a. Which point $(A \text { or } B)$ has the greater angular velocity? Explain. $B$
b. Which point $(A \text { or } B)$ has the greater linear velocity? Explain. Both points have the same linear velocity.

Umar Sohail Qureshi
Umar Sohail Qureshi
Numerade Educator
02:31

Problem 84

Given that $s, r, \theta, t, v,$ and $\omega$ are as defined in Section 4.1 determine which of the following formulas are valid.
$$\begin{array}{lll}
s=r \theta & r=\frac{s}{\theta} & v=\frac{r \theta}{t} \\
v=r \omega & v=\frac{s}{t} & \omega=\frac{\theta}{t}
\end{array}$$

Umar Sohail Qureshi
Umar Sohail Qureshi
Numerade Educator
01:36

Problem 85

A nautical mile is the length of an arc, on the earth's equator, that subtends a $1^{\prime}$ central angle. The equatorial radius of the earth is about 3960 statute miles.
a. Convert 1 nautical mile to statute miles. Round to the nearest hundredth of a statute mile.
b. Determine what percent (to the nearest 1 percent) of the earth's circumference is covered by a trip from Los Angeles, California to Honolulu, Hawaii (a distance of 2217 nautical miles).

Abigail Polmanteer
Abigail Polmanteer
Numerade Educator
01:30

Problem 86

The field of view for a camera with a 200-millimeter lens is $12^{\circ} .$ A photographer takes a photograph of a large building that is 485 feet in front of the camera. What is the approximate width, to the nearest foot, of the building that will appear in the photograph? (Hint: If the radius of an arc $A B$ is large and its central angle is small, then the length of the chord $A B$ is approximately the length of the arc $A B .$ )

Eleanor Johnson
Eleanor Johnson
Numerade Educator
01:25

Problem 87

A sector of a circle is the region bounded by radii OA and OB and the intercepted arc $A B$. See the following figure. The area of the sector is given by
$$A=\frac{1}{2} r^{2} \theta$$
(GRAPH CAN'T COPY).
where $r$ is the radius of the circle and $\theta$ is the measure of the central angle in radians.
In Exercises 87 to $90,$ find the area, to the nearest square unit, of the sector of a circle with the given radius and central angle.
$$r=5 \text { inches, } \theta=\frac{\pi}{3} \text { radians }$$

Sheryl Ezze
Sheryl Ezze
Numerade Educator
00:37

Problem 88

A sector of a circle is the region bounded by radii OA and OB and the intercepted arc $A B$. See the following figure. The area of the sector is given by
$$A=\frac{1}{2} r^{2} \theta$$
(GRAPH CAN'T COPY).
where $r$ is the radius of the circle and $\theta$ is the measure of the central angle in radians.
In Exercises 87 to $90,$ find the area, to the nearest square unit, of the sector of a circle with the given radius and central angle.
$$r=2.8 \text { feet, } \theta=\frac{5 \pi}{2} \text { radians }$$

Erika Bustos
Erika Bustos
Numerade Educator
00:38

Problem 89

A sector of a circle is the region bounded by radii OA and OB and the intercepted arc $A B$. See the following figure. The area of the sector is given by
$$A=\frac{1}{2} r^{2} \theta$$
(GRAPH CAN'T COPY).
where $r$ is the radius of the circle and $\theta$ is the measure of the central angle in radians.
In Exercises 87 to $90,$ find the area, to the nearest square unit, of the sector of a circle with the given radius and central angle.
$r=120$ centimeters, $\theta=0.65$ radian

Erika Bustos
Erika Bustos
Numerade Educator
00:51

Problem 90

A sector of a circle is the region bounded by radii OA and OB and the intercepted arc $A B$. See the following figure. The area of the sector is given by
$$A=\frac{1}{2} r^{2} \theta$$
(GRAPH CAN'T COPY).
where $r$ is the radius of the circle and $\theta$ is the measure of the central angle in radians.
In Exercises 87 to $90,$ find the area, to the nearest square unit, of the sector of a circle with the given radius and central angle.
$$r=30 \text { feet, } \theta=62^{\circ}$$

Erika Bustos
Erika Bustos
Numerade Educator
01:09

Problem 91

Find the area of the shaded portion of the circle. The radius of the circle is 9 inches.
(GRAPH CAN'T COPY).

Erika Bustos
Erika Bustos
Numerade Educator
02:39

Problem 92

Latitude describes the position of a point on the earth's surface in relation to the equator. A point on the equator has a latitude of $0^{\circ} .$ The north pole has a latitude of $90^{\circ} .$ The radius of the earth is approximately 3960 miles.
(IMAGE CAN'T COPY).
The city of New York has a latitude of $40^{\circ} 45^{\prime} \mathrm{N} .$ How far north, to the nearest 10 miles, is it from the equator? Use 3960 miles as the radius of the earth.

Umar Sohail Qureshi
Umar Sohail Qureshi
Numerade Educator
02:39

Problem 93

Latitude describes the position of a point on the earth's surface in relation to the equator. A point on the equator has a latitude of $0^{\circ} .$ The north pole has a latitude of $90^{\circ} .$ The radius of the earth is approximately 3960 miles.
(IMAGE CAN'T COPY).
The city of Miami has a latitude of $25^{\circ} 47^{\prime} \mathrm{N}$. How far north, to the nearest 10 miles, is it from the equator? Use 3960 miles as the radius of the earth.

Umar Sohail Qureshi
Umar Sohail Qureshi
Numerade Educator
02:39

Problem 94

Latitude describes the position of a point on the earth's surface in relation to the equator. A point on the equator has a latitude of $0^{\circ} .$ The north pole has a latitude of $90^{\circ} .$ The radius of the earth is approximately 3960 miles.
(IMAGE CAN'T COPY).
Assuming that the earth is a perfect sphere, and expressing your answer to three significant digits, find the distance along the earth's surface (in miles) that subtends a central angle of
a. $1^{\circ}$
b. $1^{\prime} $
c. $1^{\prime \prime}$

Umar Sohail Qureshi
Umar Sohail Qureshi
Numerade Educator
00:20

Problem 95

Determine whether the point (0,1) is a point on the circle defined by $x^{2}+y^{2}=1$

Erika Bustos
Erika Bustos
Numerade Educator
00:29

Problem 96

Determine whether the point $\left(\frac{1}{2}, \frac{\sqrt{3}}{2}\right)$ is a point on the circle defined by $x^{2}+y^{2}=1 .[1.2]$

Erika Bustos
Erika Bustos
Numerade Educator
00:36

Problem 97

Determine whether the point $\left(\frac{\sqrt{2}}{2}, \frac{\sqrt{3}}{2}\right)$ is a point on the circle defined by $x^{2}+y^{2}=1 .[1.2]$

Erika Bustos
Erika Bustos
Numerade Educator
00:23

Problem 98

Determine the circumference of a circle with a radius of 1

Erika Bustos
Erika Bustos
Numerade Educator
00:55

Problem 99

Determine whether $f(x)=x^{2}-3$ is an even function, an odd function, or a function that is neither even nor odd. [1.6]

Erika Bustos
Erika Bustos
Numerade Educator
01:20

Problem 100

Determine whether $f(x)=x^{3}-x^{2}$ is an even function, an odd function, or a function that is neither even nor odd. [1.6]

Erika Bustos
Erika Bustos
Numerade Educator