Calculus an Applied Approach

Ron Larson, David C, Falvo

Chapter 8

Trigonometric Functions - all with Video Answers

Educators

Section 1

Radian Measure of Angles

Problem 1

determine two coterminal angles (one positive and one negative) for each angle. Give the answers in degrees.

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Problem 2

determine two coterminal angles (one positive and one negative) for each angle. Give the answers in degrees.

Harsh Gadhiya

Numerade Educator

Problem 3

determine two coterminal angles (one positive and one negative) for each angle. Give the answers in degrees.

Harsh Gadhiya

Numerade Educator

Problem 4

determine two coterminal angles (one positive and one negative) for each angle. Give the answers in degrees.

Harsh Gadhiya

Numerade Educator

Problem 5

determine two coterminal angles (one positive and one negative) for each angle. Give the answers in radians.

Harsh Gadhiya

Numerade Educator

Problem 6

determine two coterminal angles (one positive and one negative) for each angle. Give the answers in radians.

Harsh Gadhiya

Numerade Educator

Problem 7

determine two coterminal angles (one positive and one negative) for each angle. Give the answers in radians.

Harsh Gadhiya

Numerade Educator

Problem 8

determine two coterminal angles (one positive and one negative) for each angle. Give the answers in radians.

Harsh Gadhiya

Numerade Educator

Problem 9

express the angle in radian measure as a multiple of $\pi .$ Use a calculator to verify your result.
$$
30^{\circ}
$$

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Problem 10

express the angle in radian measure as a multiple of $\pi .$ Use a calculator to verify your result.
$$
60^{\circ}
$$

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Problem 11

express the angle in radian measure as a multiple of $\pi .$ Use a calculator to verify your result.
$$
270^{\circ}
$$

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Problem 12

express the angle in radian measure as a multiple of $\pi .$ Use a calculator to verify your result.
$$
210^{\circ}
$$

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Problem 13

express the angle in radian measure as a multiple of $\pi .$ Use a calculator to verify your result.
$$
315^{\circ}
$$

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Numerade Educator

Problem 14

express the angle in radian measure as a multiple of $\pi .$ Use a calculator to verify your result.
$$
120^{\circ}
$$

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Problem 15

express the angle in radian measure as a multiple of $\pi .$ Use a calculator to verify your result.
$$
-20^{\circ}
$$

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Problem 16

express the angle in radian measure as a multiple of $\pi .$ Use a calculator to verify your result.
$$
-240^{\circ}
$$

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Numerade Educator

Problem 17

express the angle in radian measure as a multiple of $\pi .$ Use a calculator to verify your result.
$$
-270^{\circ}
$$

Harsh Gadhiya

Numerade Educator

Problem 18

express the angle in radian measure as a multiple of $\pi .$ Use a calculator to verify your result.
$$
-315^{\circ}
$$

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Numerade Educator

Problem 19

express the angle in radian measure as a multiple of $\pi .$ Use a calculator to verify your result.
$$
330^{\circ}
$$

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Problem 20

express the angle in radian measure as a multiple of $\pi .$ Use a calculator to verify your result.
$$
405^{\circ}
$$

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Problem 21

express the angle in degree measure. Use a calculator to verify your result.
$$
\frac{5 \pi}{2}
$$

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Problem 22

express the angle in degree measure. Use a calculator to verify your result.
$$
\frac{5 \pi}{4}
$$

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Problem 23

express the angle in degree measure. Use a calculator to verify your result.
$$
\frac{7 \pi}{3}
$$

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Problem 24

express the angle in degree measure. Use a calculator to verify your result.
$$
\frac{\pi}{9}
$$

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Numerade Educator

Problem 25

express the angle in degree measure. Use a calculator to verify your result.
$$
-\frac{\pi}{12}
$$

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Numerade Educator

Problem 26

express the angle in degree measure. Use a calculator to verify your result.
$$
-\frac{7 \pi}{4}
$$

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Numerade Educator

Problem 27

express the angle in degree measure. Use a calculator to verify your result.
$$
\frac{9 \pi}{4}
$$

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Problem 28

express the angle in degree measure. Use a calculator to verify your result.
$$
-\frac{3 \pi}{2}
$$

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Problem 29

express the angle in degree measure. Use a calculator to verify your result.
$$
\frac{19 \pi}{6}
$$

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Problem 30

express the angle in degree measure. Use a calculator to verify your result.
$$
\frac{8 \pi}{3}
$$

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Numerade Educator

Problem 31

find the indicated measure of the angle. Express radian measure as a multiple of $\pi .$
$$
-270^{\circ}
$$

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Problem 32

find the indicated measure of the angle. Express radian measure as a multiple of $\pi .$
$$
\frac{\pi}{9}
$$

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Numerade Educator

Problem 33

find the indicated measure of the angle. Express radian measure as a multiple of $\pi .$
$$
144^{\circ}
$$

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Problem 34

find the indicated measure of the angle. Express radian measure as a multiple of $\pi .$
$$
-\frac{7 \pi}{12}
$$

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Numerade Educator

Problem 35

solve the triangle for the indicated side and/or angle.

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Problem 36

solve the triangle for the indicated side and/or angle.

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Problem 37

solve the triangle for the indicated side and/or angle.

Harsh Gadhiya

Numerade Educator

Problem 38

solve the triangle for the indicated side and/or angle.

Harsh Gadhiya

Numerade Educator

Problem 39

solve the triangle for the indicated side and/or angle.

Harsh Gadhiya

Numerade Educator

Problem 40

solve the triangle for the indicated side and/or angle.

Harsh Gadhiya

Numerade Educator

Problem 41

solve the triangle for the indicated side and/or angle.

Harsh Gadhiya

Numerade Educator

Problem 42

solve the triangle for the indicated side and/or angle.

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Problem 43

find the area of the equilateral triangle with sides of length $s$.
$$
s=4 \mathrm{in}
$$

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Problem 44

find the area of the equilateral triangle with sides of length $s$.
$$
s=8 \mathrm{m}
$$

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Problem 45

find the area of the equilateral triangle with sides of length $s$.
$$
s=5 \mathrm{ft}
$$

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Problem 46

find the area of the equilateral triangle with sides of length $s$.
$$
s=12 \mathrm{cm}
$$

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Problem 47

Height A person 6 feet tall standing 16 feet from a streetlight casts a shadow 8 feet long (see figure). What is the height of the streetlight?

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Problem 48

Length A guy wire is stretched from a broadcasting tower at a point 200 feet above the ground to an anchor 125 feet from the base (see figure). How long is the wire?

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Problem 49

Arc Length Let $r$ represent the radius of a circle, $\theta$ the central angle (measured in radians), and $s$ the length of the are intercepted by the angle (see figure). Use the relationship $\theta=s / r$ and a spreadsheet to complete the table.

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Problem 50

Arc Length The minute hand on a clock is $3 \frac{1}{2}$ inches long (see figure). Through what distance does the tip of the minute hand move in 25 minutes?

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Problem 51

Distance A tractor tire that is 5 feet in diameter $d$ is partially filled with a liquid ballast for additional traction. To check the air pressure, the tractor operator rotates the tire until the valve stem is at the top so that the liquid will not enter the gauge. On a given occasion, the operator notes that the tire must be rotated $80^{\circ}$ to have the stem in the
proper position ( see figure).
(a) Find the radian measure of this rotation.
(b) How far must the tractor be moved to get the valve stem in the proper position?

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Problem 52

Speed of Revolution A compact disc can have an angular speed up to 3142 radians per minute.
(a) At this angular speed, how many revolutions per minute would the CD make?
(b) How long would it take the CD to make $10,000$ revolutions?

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Problem 53

use the following information. A sector of a circle is the region bounded by two radii of the circle and their intercepted arc (see figure).
For a circle of radius $r,$ the area $A$ of a sector of the circle with central angle $\theta$ (measured in radians) is given by $A=\frac{1}{2} r^{2} \theta$

Sprinkler System A sprinkler system on a farm is set to spray water over a distance of 70 feet and rotates through an angle of $120^{\circ} .$ Find the area of the region.

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Problem 54

use the following information. A sector of a circle is the region bounded by two radii of the circle and their intercepted arc (see figure).
For a circle of radius $r,$ the area $A$ of a sector of the circle with central angle $\theta$ (measured in radians) is given by $A=\frac{1}{2} r^{2} \theta$

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

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Problem 55

determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.

An angle whose measure is $75^{\circ}$ is obtuse.

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Problem 56

determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.

$\theta=-35^{\circ}$ is coterminal to $325^{\circ}$

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Problem 57

determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.

A right triangle can have one angle whose measure is $89^{\circ} .$

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Problem 58

determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.

An angle whose measure is $\pi$ radians is a straight angle.

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