Precalculus

David Cohen, Theodore Lee, David Sklar

Chapter 7

Trigonometric Functions of Real Numbers - all with Video Answers

Educators

Section 1

Radian Measure

Problem 1

Use the definition $\theta=s / r$ to determine the radian measure of each angle.
(Circle can't copy)

Katelyn Chen

Katelyn Chen

Numerade Educator

Problem 2

Use the definition $\theta=s / r$ to determine the radian measure of each angle.
(Circle can't copy)

Katelyn Chen

Numerade Educator

Problem 3

Use the definition $\theta=s / r$ to determine the radian measure of each angle.
(Circle can't copy)

Katelyn Chen

Numerade Educator

Problem 4

Use the definition $\theta=s / r$ to determine the radian measure of each angle.
(Circle can't copy)

Katelyn Chen

Numerade Educator

Problem 5

Convert to radian measure. Express your answers both in terms of $\pi$ and as decimal approximations rounded to two decimal places.
(a) $45^{\circ}$
(b) $90^{\circ}$
(c) $135^{\circ}$

Katelyn Chen

Numerade Educator

Problem 6

Convert to radian measure. Express your answers both in terms of $\pi$ and as decimal approximations rounded to two decimal places.
(a) $30^{\circ}$
(b) $150^{\circ}$
(c) $300^{\circ}$

Katelyn Chen

Numerade Educator

Problem 7

Convert to radian measure. Express your answers both in terms of $\pi$ and as decimal approximations rounded to two decimal places.
$$\begin{array}{llll}
\text { a) } 0^{\circ} & \text { (b) } 360^{\circ} & \text { (c) } 450^{\circ}
\end{array}$$

Katelyn Chen

Numerade Educator

Problem 8

Convert to radian measure. Express your answers both in terms of $\pi$ and as decimal approximations rounded to two decimal places.
(a) $36^{\circ}$
(b) $35^{\circ}$
(c) $720^{\circ}$

Katelyn Chen

Numerade Educator

Problem 9

convert the radian measures to degrees.
(a) $\pi / 12$
(b) $\pi / 6$
(c) $\pi / 4$

Katelyn Chen

Numerade Educator

Problem 10

convert the radian measures to degrees.
$$\begin{array}{llll} \text { (a) } 3 \pi & \text { (b) } 3 \pi / 2 & \text { (c) } 2 \pi \end{array}$$

Katelyn Chen

Numerade Educator

Problem 11

Convert the radian measures to degrees.
(a) $\pi / 3$
(b) $5 \pi / 3$
(c) $4 \pi$

Katelyn Chen

Numerade Educator

Problem 12

Convert the radian measures to degrees.
(a) $5 \pi / 6$
(b) $11 \pi / 6$
(c) 0

Katelyn Chen

Numerade Educator

Problem 13

Convert the radian measures to degrees. Round the answers to two decimal places.
$\begin{array}{llll}\text { (a) } 2 & \text { (b) } 3 & \text { (c) } \pi^{2}\end{array}$

Sriram Soundarrajan

Sriram Soundarrajan

Numerade Educator

Problem 14

Convert the radian measures to degrees. Round the answers to two decimal places.
(a) 1.32
(b) 0.96
(c) $1 / \pi$

Katelyn Chen

Numerade Educator

Problem 15

Suppose that the radian measure of an angle is $3 / 2 .$ Without using a calculator or tables, determine if this angle is larger or smaller than a right angle. Hint : What is the radian measure of a right angle?

Katelyn Chen

Numerade Educator

Problem 16

Two angles in a triangle have radian measure $\pi / 5$ and $\pi / 6$ What is the radian measure of the third angle?

Katelyn Chen

Numerade Educator

Problem 17

Refer to the following figure, which shows all of the angles from $0^{\circ}$ to $360^{\circ}$ that are multiples of $30^{\circ}$ or $45^{\circ}$
In the figure, relabel the angles in Quadrants I and II using radian measure.

Katelyn Chen

Numerade Educator

Problem 18

Refer to the following figure, which shows all of the angles from $0^{\circ}$ to $360^{\circ}$ that are multiples of $30^{\circ}$ or $45^{\circ}$
In the figure, relabel the angles in Quadrants III and IV using radian measure.

Katelyn Chen

Numerade Educator

Problem 19

Complete the tables.
(Table can't copy)

Shaza Hammoud

Numerade Educator

Problem 20

Complete the tables.
(Table can't copy)

Shaza Hammoud

Numerade Educator

Problem 21

Use Figure 6 to approximate the given trigonometric values to within successive tenths. Then use a calculator to compute the values to the nearest hundredth.
$$\cos 1 \text { and } \sin 1$$

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 22

Use Figure 6 to approximate the given trigonometric values to within successive tenths. Then use a calculator to compute the values to the nearest hundredth.
$$\cos 2 \text { and } \sin 2$$

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 23

Use Figure 6 to approximate the given trigonometric values to within successive tenths. Then use a calculator to compute the values to the nearest hundredth.
$$\cos (-1) \text { and } \sin (-1)$$

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 24

Use Figure 6 to approximate the given trigonometric values to within successive tenths. Then use a calculator to compute the values to the nearest hundredth.
$$\cos (-2) \text { and } \sin (-2)$$

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 25

Use Figure 6 to approximate the given trigonometric values to within successive tenths. Then use a calculator to compute the values to the nearest hundredth.
$$\cos 4 \text { and } \sin 4$$

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 26

Use Figure 6 to approximate the given trigonometric values to within successive tenths. Then use a calculator to compute the values to the nearest hundredth.
$$\cos 5 \text { and } \sin 5$$

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 27

Use Figure 6 to approximate the given trigonometric values to within successive tenths. Then use a calculator to compute the values to the nearest hundredth.
$$\cos (-4) \text { and } \sin (-4)$$

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 28

Use Figure 6 to approximate the given trigonometric values to within successive tenths. Then use a calculator to compute the values to the nearest hundredth.
$$\cos (-5) \text { and } \sin (-5)$$

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 29

Use Figure 6 to approximate the given trigonometric values to within successive tenths. Then use a calculator to compute the values to the nearest hundredth.
$$\sin (1+2 \pi)$$

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 30

Use Figure 6 to approximate the given trigonometric values to within successive tenths. Then use a calculator to compute the values to the nearest hundredth.
$$\sin (2+2 \pi)$$

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 31

Evaluate each expression (as in Example 8).
(a) $\cos (\pi / 3)$
(c) $\sin (\pi / 3)$
(b) $\cos (-\pi / 3)$
(d) $\sin (-\pi / 3)$

Zachary Mitchell

Zachary Mitchell

Numerade Educator

Problem 32

Evaluate each expression (as in Example 8).
(a) $\cos (5 \pi / 3)$
(c) $\sin (5 \pi / 3)$
(b) $\cos (-5 \pi / 3)$
(d) $\sin (-5 \pi / 3)$

Zachary Mitchell

Zachary Mitchell

Numerade Educator

Problem 33

Evaluate each expression (as in Example 8).
(a) $\cos (4 \pi / 3)$
(c) $\sin (4 \pi / 3)$
(b) $\cos (-4 \pi / 3)$
(d) $\sin (-4 \pi / 3)$

Zachary Mitchell

Zachary Mitchell

Numerade Educator

Problem 34

Evaluate each expression (as in Example 8).
(a) $\cos (2 \pi / 3)$
(c) $\sin (2 \pi / 3)$
(b) $\cos (-2 \pi / 3)$
(d) $\sin (-2 \pi / 3)$

Zachary Mitchell

Zachary Mitchell

Numerade Educator

Problem 35

Evaluate each expression (as in Example 8).
(a) $\cos (5 \pi / 4)$
(c) $\sin (5 \pi / 4)$
(b) $\cos (-5 \pi / 4)$
(d) $\sin (-5 \pi / 4)$

Zachary Mitchell

Zachary Mitchell

Numerade Educator

Problem 36

Evaluate each expression (as in Example 8).
(a) $\cos (17 \pi / 6)$
(c) $\sin (17 \pi / 6)$
(b) $\cos (17 \pi / 6)$
(d) $\sin (-17 \pi / 6)$

Gregory Higby

Numerade Educator

Problem 37

Evaluate each expression (as in Example 8).
(a) $\sec (4 \pi / 3)$
(c) $\tan (4 \pi / 3)$
(b) $\csc (-4 \pi / 3)$
(d) $\cot (-4 \pi / 3)$

Zachary Mitchell

Zachary Mitchell

Numerade Educator

Problem 38

Evaluate each expression (as in Example 8).
(a) $\sec (7 \pi / 4)$
(c) $\tan (7 \pi / 4)$
(b) $\csc (-7 \pi / 4)$
(d) $\cot (-7 \pi / 4)$

Zachary Mitchell

Zachary Mitchell

Numerade Educator

Problem 39

Evaluate each expression (as in Example 8).
(a) $\sec (17 \pi / 6)$
(c) $\tan (17 \pi / 6)$
(b) $\csc (-17 \pi / 6)$
(d) $\cot (-17 \pi / 6)$

Nicole C

Numerade Educator

Problem 40

Evaluate each expression (as in Example 8).
(a) $\sec (3 \pi / 4)$
(c) $\tan (3 \pi / 4)$
(b) $\csc (-3 \pi / 4)$
(d) $\cot (-3 \pi / 4)$

Zachary Mitchell

Zachary Mitchell

Numerade Educator

Problem 41

Suppose that you have two sticks and a piece of wire, each of length $1 \mathrm{ft}$, fastened at the ends to form an equilateral triangle; see Figure A. If side $\overline{B C}$ is bent out to form an arc of a circle with center $A,$ then the angle at $A$ will decrease from $60^{\circ}$ to something less. See Figure $\mathrm{B}$. What is the measure of this new angle at $A$ in both radians and degrees?

Katelyn Chen

Numerade Educator

Problem 42

(a) When a clock reads $4: 00,$ what is the radian measure of the (smaller) angle between the hour hand and the minute hand?
(b) When a clock reads $5: 30,$ what is the radian measure of the (smaller) angle between the hour hand and the minute hand?

Sirat Shah

Numerade Educator

Problem 43

Are there any real numbers $x$ with the property that $x$ degrees equals $x$ radians? If so, find them; if not, explain why not.

Katelyn Chen

Numerade Educator

Problem 44

Are there any real numbers $x$ with the property that $x$ degrees equals $2 x$ radians? If so, find them; if not, explain why not.

Katelyn Chen

Numerade Educator