Chapter 7, The Unit Circle: Sine and Cosine Functions Video Solutions, Algebra and Trigonometry

Section 1

Angles

00:42

Problem 1

Draw an angle in standard position. Label the vertex, initial side, and terminal side.

Amrita B.

Numerade Educator

01:59

Problem 2

Explain why there are an infinite number of angles that are coterminal to a certain angle.

Ernest C.

Numerade Educator

01:00

Problem 3

State what a positive or negative angle signifies, and explain how to draw each.

Amrita B.

Numerade Educator

05:04

Problem 4

How does radian measure of an angle compare to the degree measure? Include an explanation of 1 radian in your paragraph.

Ernest C.

Numerade Educator

00:47

Problem 5

Explain the differences between linear speed and angular speed when describing motion along a circular path.

Amrita B.

Numerade Educator

00:48

Problem 6

For the following exercises, draw an angle in standard position with the given measure.
$$30^{\circ}$$

Ernest C.

Numerade Educator

00:58

Problem 7

For the following exercises, draw an angle in standard position with the given measure.
$$300^{\circ}$$

Amrita B.

Numerade Educator

00:46

Problem 8

For the following exercises, draw an angle in standard position with the given measure.
$$-80^{\circ}$$

Ernest C.

Numerade Educator

00:44

Problem 9

For the following exercises, draw an angle in standard position with the given measure.
$$135^{\circ}$$

Amrita B.

Numerade Educator

01:18

Problem 10

For the following exercises, draw an angle in standard position with the given measure.
$$-150^{\circ}$$

Ernest C.

Numerade Educator

01:02

Problem 11

For the following exercises, draw an angle in standard position with the given measure.
$$\frac{2 \pi}{3}$$

Amrita B.

Numerade Educator

01:18

Problem 12

For the following exercises, draw an angle in standard position with the given measure.
$$\frac{7 \pi}{4}$$

Ernest C.

Numerade Educator

00:56

Problem 13

For the following exercises, draw an angle in standard position with the given measure.
$$\frac{5 \pi}{6}$$

Amrita B.

Numerade Educator

00:34

Problem 14

For the following exercises, draw an angle in standard position with the given measure.
$$\frac{\pi}{2}$$

Ernest C.

Numerade Educator

01:08

Problem 15

For the following exercises, draw an angle in standard position with the given measure.
$$-\frac{\pi}{10}$$

Amrita B.

Numerade Educator

01:04

Problem 16

For the following exercises, draw an angle in standard position with the given measure.
$$415^{\circ}$$

Ernest C.

Numerade Educator

01:06

Problem 17

For the following exercises, draw an angle in standard position with the given measure.
$$-120^{\circ}$$

Amrita B.

Numerade Educator

01:04

Problem 18

For the following exercises, draw an angle in standard position with the given measure.
$$-315^{\circ}$$

Ernest C.

Numerade Educator

01:02

Problem 19

For the following exercises, draw an angle in standard position with the given measure.
$$\frac{22 \pi}{3}$$

Amrita B.

Numerade Educator

01:27

Problem 20

For the following exercises, draw an angle in standard position with the given measure.
$$-\frac{\pi}{6}$$

Ernest C.

Numerade Educator

00:46

Problem 21

For the following exercises, draw an angle in standard position with the given measure.
$$-\frac{4 \pi}{3}$$

Amrita B.

Numerade Educator

01:22

Problem 22

For the following exercises, refer to Figure $25 .$ Round to For the following exercises, refer to Figure $26 .$ Round to two decimal places. two decimal places. Find the arc length.

Bryce S.

Numerade Educator

01:30

Problem 23

For the following exercises, refer to Figure $25 .$ Round to For the following exercises, refer to Figure $26 .$ Round to two decimal places. two decimal places. Find the area of the sector.

Bryce S.

Numerade Educator

00:57

Problem 24

For the following exercises, refer to Figure $25 .$ Round to For the following exercises, refer to Figure $26 .$ Round to two decimal places. two decimal places. Find the arc length.

Bryce S.

Numerade Educator

01:17

Problem 25

For the following exercises, refer to Figure $25 .$ Round to For the following exercises, refer to Figure $26 .$ Round to two decimal places. two decimal places. Find the area of the sector.

Bryce S.

Numerade Educator

01:03

Problem 26

For the following exercises, convert angles in radians to degrees.
$\frac{3 \pi}{4}$ radians

Ernest C.

Numerade Educator

00:30

Problem 27

For the following exercises, convert angles in radians to degrees.
$\frac{\pi}{9}$ radians

Amrita B.

Numerade Educator

00:44

Problem 28

For the following exercises, convert angles in radians to degrees.
$-\frac{5 \pi}{4}$ radians

Ernest C.

Numerade Educator

00:33

Problem 29

For the following exercises, convert angles in radians to degrees.
$\frac{\pi}{3}$ radians

Amrita B.

Numerade Educator

00:39

Problem 30

For the following exercises, convert angles in radians to degrees.
$-\frac{7 \pi}{3}$ radians

Ernest C.

Numerade Educator

00:34

Problem 31

For the following exercises, convert angles in radians to degrees.
$-\frac{5 \pi}{12}$ radians

Amrita B.

Numerade Educator

00:42

Problem 32

For the following exercises, convert angles in radians to degrees.
$\frac{11 \pi}{6}$ radians

Ernest C.

Numerade Educator

00:35

Problem 33

For the following exercises, convert angles in degrees to radians.
$$90^{\circ}$$

Amrita B.

Numerade Educator

00:25

Problem 34

For the following exercises, convert angles in degrees to radians.
$$100^{\circ}$$

Ernest C.

Numerade Educator

00:38

Problem 35

For the following exercises, convert angles in degrees to radians.
$$-540^{\circ}$$

Amrita B.

Numerade Educator

00:29

Problem 36

For the following exercises, convert angles in degrees to radians.
$$-120^{\circ}$$

Ernest C.

Numerade Educator

00:27

Problem 37

For the following exercises, convert angles in degrees to radians.
$$180^{\circ}$$

Amrita B.

Numerade Educator

00:45

Problem 38

For the following exercises, convert angles in degrees to radians.
$$-315^{\circ}$$

Ernest C.

Numerade Educator

00:32

Problem 39

For the following exercises, convert angles in degrees to radians.
$$150^{\circ}$$

Amrita B.

Numerade Educator

01:07

For the following exercises, use to given information to find the length of a circular arc. Round to two decimal places. Find the length of the arc of a circle of radius 12 inches subtended by a central angle of $\frac{\pi}{4}$ radians.

Ernest C.

Numerade Educator

00:42

Problem 41

For the following exercises, use to given information to find the length of a circular arc. Round to two decimal places. Find the length of the arc of a circle of radius 5.02 miles subtended by the central angle of $\frac{\pi}{3} .$

Amrita B.

Numerade Educator

00:52

Problem 42

For the following exercises, use to given information to find the length of a circular arc. Round to two decimal places. Find the length of the arc of a circle of diameter 14 meters subtended by the central angle of $\frac{5 \pi}{6}$.

Ernest C.

Numerade Educator

01:04

Problem 43

For the following exercises, use to given information to find the length of a circular arc. Round to two decimal places. Find the length of the arc of a circle of radius 10 centimeters subtended by the central angle of $50^{\circ}$.

Amrita B.

Numerade Educator

01:41

Problem 44

For the following exercises, use to given information to find the length of a circular arc. Round to two decimal places. Find the length of the arc of a circle of radius 5 inches subtended by the central angle of $220^{\circ}$.

Ernest C.

Numerade Educator

00:59

Problem 45

For the following exercises, use to given information to find the length of a circular arc. Round to two decimal places. Find the length of the arc of a circle of diameter 12 meters subtended by the central angle is $63^{\circ} .$

Amrita B.

Numerade Educator

01:25

Problem 46

For the following exercises, use the given information to find the area of the sector. Round to four decimal places. A sector of a circle has a central angle of $45^{\circ}$ and a radius $6 \mathrm{cm}$.

Ernest C.

Numerade Educator

01:02

Problem 47

For the following exercises, use the given information to find the area of the sector. Round to four decimal places. A sector of a circle has a central angle of $30^{\circ}$ and a radius of $20 \mathrm{cm} .$

Amrita B.

Numerade Educator

00:57

Problem 48

For the following exercises, use the given information to find the area of the sector. Round to four decimal places. A sector of a circle with diameter 10 feet and an angle of $\frac{\pi}{2}$ radians.

Ernest C.

Numerade Educator

00:41

Problem 49

For the following exercises, use the given information to find the area of the sector. Round to four decimal places. A sector of a circle with radius of 0.7 inches and an angle of $\pi$ radians.

Amrita B.

Numerade Educator

00:40

Problem 50

For the following exercises, find the angle between $0^{\circ}$ and $360^{\circ}$ that is coterminal to the given angle. $$-40^{\circ}$$

Ernest C.

Numerade Educator

01:11

Problem 51

For the following exercises, find the angle between $0^{\circ}$ and $360^{\circ}$ that is coterminal to the given angle. $$-110^{\circ}$$

Bryce S.

Numerade Educator

00:27

Problem 52

For the following exercises, find the angle between $0^{\circ}$ and $360^{\circ}$ that is coterminal to the given angle. $$700^{\circ}$$

Ernest C.

Numerade Educator

00:48

Problem 53

For the following exercises, find the angle between $0^{\circ}$ and $360^{\circ}$ that is coterminal to the given angle. $$1400^{\circ}$$

Amrita B.

Numerade Educator

00:33

Problem 54

For the following exercises, find the angle between 0 and $2 \pi$ in radians that is coterminal to the given angle. $$-\frac{\pi}{9}$$

Ernest C.

Numerade Educator

00:38

Problem 55

For the following exercises, find the angle between 0 and $2 \pi$ in radians that is coterminal to the given angle. $$\frac{10 \pi}{3}$$

Amrita B.

Numerade Educator

00:27

Problem 56

For the following exercises, find the angle between 0 and $2 \pi$ in radians that is coterminal to the given angle. $$\frac{13 \pi}{6}$$

Ernest C.

Numerade Educator

00:44

Problem 57

For the following exercises, find the angle between 0 and $2 \pi$ in radians that is coterminal to the given angle. $$\frac{44 \pi}{9}$$

Amrita B.

Numerade Educator

02:35

Problem 58

A truck with 32 -inch diameter wheels is traveling at $60 \mathrm{mi} / \mathrm{h} .$ Find the angular speed of the wheels in rad/min. How many revolutions per minute do the wheels make?

Bryce S.

Numerade Educator

03:08

Problem 59

A bicycle with 24 -inch diameter wheels is traveling at $15 \mathrm{mi} / \mathrm{h} .$ Find the angular speed of the wheels in rad/ min. How many revolutions per minute do the wheels make?

Bryce S.

Numerade Educator

02:39

Problem 60

A wheel of radius 8 inches is rotating $15^{\circ} / \mathrm{s}$. What is the linear speed $v,$ the angular speed in $\mathrm{RPM}$, and the angular speed in rad/s?

Bryce S.

Numerade Educator

02:00

Problem 61

A wheel of radius 14 inches is rotating 0.5 rad/s. What is the linear speed $v,$ the angular speed in $\mathrm{RPM}$, and the angular speed in deg/s?

Bryce S.

Numerade Educator

02:01

Problem 62

A CD has diameter of 120 millimeters. When playing audio, the angular speed varies to keep the linear speed constant where the disc is being read. When reading along the outer edge of the disc, the angular speed is about 200 RPM (revolutions per minute). Find the linear speed.

Bryce S.

Numerade Educator

02:09

Problem 63

When being burned in a writable CD-R drive, the angular speed of a CD varies to keep the linear speed constant where the disc is being written. When writing along the outer edge of the disc, the angular speed of one drive is about 4,800 RPM (revolutions per minute). Find the linear speed if the CD has diameter of 120 millimeters.

Bryce S.

Numerade Educator

01:32

Problem 64

A person is standing on the equator of Earth (radius 3960 miles ). What are his linear and angular speeds?

Bryce S.

Numerade Educator

01:45

Problem 65

Find the distance along an arc on the surface of Earth that subtends a central angle of 5 minutes $\left(1 \text { minute }=\frac{1}{60} \text { degree }\right) .$ The radius of Earth is $3,960 \mathrm{mi}$.

Bryce S.

Numerade Educator

01:40

Problem 66

Find the distance along an arc on the surface of Earth that subtends a central angle of 7 minutes $\left(1 \text { minute }=\frac{1}{60} \text { degree }\right) .$ The radius of Earth is 3,960 miles.

Bryce S.

Numerade Educator

01:28

Problem 67

Consider a clock with an hour hand and minute hand. What is the measure of the angle the minute hand traces in 20 minutes?

Bryce S.

Numerade Educator

01:39

Problem 68

Two cities have the same longitude. The latitude of city A is 9.00 degrees north and the latitude of city $B$ is 30.00 degree north. Assume the radius of the earth is 3960 miles. Find the distance between the two cities.

Bryce S.

Numerade Educator

02:15

Problem 69

A city is located at 40 degrees north latitude. Assume the radius of the earth is 3960 miles and the earth rotates once every 24 hours. Find the linear speed of a person who resides in this city.

Suzanne W.

Numerade Educator

02:46

Problem 70

A city is located at 75 degrees north latitude. Assume the radius of the earth is 3960 miles and the earth rotates once every 24 hours. Find the linear speed of a person who resides in this city.

Abdul V.

Numerade Educator

01:56

Problem 71

Find the linear speed of the moon if the average distance between the earth and moon is 239,000 miles, assuming the orbit of the moon is circular and requires about 28 days. Express answer in miles per hour.

Bryce S.

Numerade Educator

04:03

Problem 72

A bicycle has wheels 28 inches in diameter. $\mathrm{A}$ tachometer determines that the wheels are rotating at 180 RPM (revolutions per minute). Find the speed the bicycle is travelling down the road.

Charles C.

Numerade Educator

01:20

Problem 73

A car travels 3 miles. Its tires make 2640 revolutions. What is the radius of a tire in inches?

Mrinal R.

Numerade Educator

01:57

Problem 74

A wheel on a tractor has a 24 -inch diameter. How many revolutions does the wheel make if the tractor travels 4 miles?

Bryce S.

Numerade Educator