1. Measuring Angles

Convert each radian measure to degrees.

8π/3

190

Convert each radian measure to degrees.

-11π/18

178

Convert each degree measure to radians. If applicable, round to the nearest thousandth. See Example 1(c).

39°

191

Convert each degree measure to radians. If applicable, round to the nearest thousandth. See Example 1(c).

42.5°

158

Convert each degree measure to radians. If applicable, round to the nearest thousandth. See Example 1(c).

139° 10'

197

Convert each degree measure to radians. If applicable, round to the nearest thousandth. See Example 1(c).

174° 50'

177

Convert each degree measure to radians. If applicable, round to the nearest thousandth. See Example 1(c).

64.29°

188

Convert each degree measure to radians. If applicable, round to the nearest thousandth. See Example 1(c).

85.04°

223

Convert each degree measure to radians. If applicable, round to the nearest thousandth. See Example 1(c).

56° 25'

159

Convert each degree measure to radians. If applicable, round to the nearest thousandth. See Example 1(c).

122° 37'

192

Convert each degree measure to radians. If applicable, round to the nearest thousandth. See Example 1(c).

-47.69°

216

Convert each radian measure to degrees. Write answers to the nearest minute. See Example 2(c).

2

166

Convert each radian measure to degrees. Write answers to the nearest minute. See Example 2(c).

5

183

Convert each radian measure to degrees. Write answers to the nearest minute. See Example 2(c).

3.06

183

Convert each radian measure to degrees. Write answers to the nearest minute. See Example 2(c).

0.3417

179

Convert each radian measure to degrees. Write answers to the nearest minute. See Example 2(c).

9.84763

166

Convert each radian measure to degrees. Write answers to the nearest minute. See Example 2(c).

-5.01095

166

Find each exact function value. See Example 3.

sin π/3

177

Find each exact function value. See Example 3.

tan π/4

176

Find each exact function value. See Example 3.

sec π/6

209

Find each exact function value. See Example 3.

sin π/2

191

Open Question

Find the exact values of s in the given interval that satisfy the given condition.

[0, 2π) ; sin s = -√3/ 2

247

Find each exact function value. See Example 3.

tan 5π/3

218

Find each exact function value. See Example 3.

sin 5π/6

178

Find each exact function value. See Example 3.

cos 3π

216

Find each exact function value. See Example 3.

sin (-8π/ 3)

202

Find each exact function value. See Example 3.

sin (-7π/ 6)

181

Find each exact function value. See Example 3.

tan (-14π/ 3)

171

Work each problem.

Consider each angle in standard position having the given radian measure. In what quadrant does the terminal side lie?

3

226

Give an expression that generates all angles coterminal with an angle of π/2 radians. Let n represent any integer.

296

Through how many radians does the minute hand on a clock rotate in (a) 12 hr and (b) 3 hr?

234

In Exercises 21–28, an object moves in simple harmonic motion described by the given equation, where t is measured in seconds and d in inches. In each exercise, find the following: a. the maximum displacement b. the frequency c. the time required for one cycle. d = 10 cos 2πt

345

In Exercises 21–28, an object moves in simple harmonic motion described by the given equation, where t is measured in seconds and d in inches. In each exercise, find the following: a. the maximum displacement b. the frequency c. the time required for one cycle. d = −8 cos π/2 t

327

In Exercises 21–28, an object moves in simple harmonic motion described by the given equation, where t is measured in seconds and d in inches. In each exercise, find the following: a. the maximum displacement b. the frequency c. the time required for one cycle. d = 1/3 sin 2t

271

In Exercises 21–28, an object moves in simple harmonic motion described by the given equation, where t is measured in seconds and d in inches. In each exercise, find the following: a. the maximum displacement b. the frequency c. the time required for one cycle. d = −4 sin 3π/2 t

408

In Exercises 37–40, an object moves in simple harmonic motion described by the given equation, where t is measured in seconds and d in inches. In each exercise, graph one period of the equation. Then find the following: a. the maximum displacement b. the frequency c. the time required for one cycle d. the phase shift of the motion. d = 3 cos(πt + π/2)

278

In Exercises 37–40, an object moves in simple harmonic motion described by the given equation, where t is measured in seconds and d in inches. In each exercise, graph one period of the equation. Then find the following: a. the maximum displacement b. the frequency c. the time required for one cycle d. the phase shift of the motion. d = − 1/2 sin(πt/4 − π/2)

344

In Exercises 1–8, use the given vectors to find v⋅w and v⋅v. v = -6i - 5j, w = -10i - 8j

203

Work each problem.

Consider each angle in standard position having the given radian measure. In what quadrant does the terminal side lie?

4

170

Work each problem.

Consider each angle in standard position having the given radian measure. In what quadrant does the terminal side lie?

-2

197

Work each problem.

Consider each angle in standard position having the given radian measure. In what quadrant does the terminal side lie?

7

206

Give an expression that generates all angles coterminal with an angle of π/6 radian. Let n represent any integer.

200

Convert each degree measure to radians. Leave answers as multiples of π .

45°

174

Convert each degree measure to radians. Leave answers as multiples of π.

175°

178

Convert each degree measure to radians. Leave answers as multiples of π.

800°

179

CONCEPT PREVIEW In each figure, find the measures of the numbered angles, given that lines m and n are parallel.

110

CONCEPT PREVIEW In each figure, find the measures of the numbered angles, given that lines m and n are parallel.

133

CONCEPT PREVIEW Name the corresponding angles and the corresponding sides of each pair of similar triangles.

121

CONCEPT PREVIEW Name the corresponding angles and the corresponding sides of each pair of similar triangles.

115

CONCEPT PREVIEW Name the corresponding angles and the corresponding sides of each pair of similar triangles. (EA is parallel to CD.)

120

CONCEPT PREVIEW Name the corresponding angles and the corresponding sides of each pair of similar triangles. (HK is parallel to EF.)

148

141

Find the measure of each marked angle. In Exercises 19–22, m and n are parallel. See Examples 1 and 2 .

147

159

Find the measure of each marked angle. In Exercises 19–22, m and n are parallel. See Examples 1 and 2 .

129

158

133

Find the measure of each marked angle. In Exercises 19–22, m and n are parallel. See Examples 1 and 2 .

123

Solve each problem. Length of a Road A camera is located on a satellite with its lens positioned at C in the figure. Length PC represents the distance from the lens to the film PQ, and BA represents a straight road on the ground. Use the measurements given in the figure to find the length of the road. (Data from Kastner, B., Space Mathematics, NASA.)

137

Find the measure of each marked angle. In Exercises 19–22, m and n are parallel. See Examples 1 and 2 .

139

Find all unknown angle measures in each pair of similar triangles.

187

Find the measure of each marked angle. In Exercises 19–22, m and n are parallel. See Examples 1 and 2 .

140

Find the unknown side lengths in each pair of similar triangles.

246

Find the measure of each marked angle. In Exercises 19–22, m and n are parallel. See Examples 1 and 2 .

137

In each figure, there are two similar triangles. Find the unknown measurement. Give any approximation to the nearest tenth.

160

The measures of two angles of a triangle are given. Find the measure of the third angle. See Example 2. 37° , 52°

148

Length of a Shadow If a tree 20 ft tall casts a shadow 8 ft long, how long would the shadow of a 30-ft tree be at the same time and place?

152

The measures of two angles of a triangle are given. Find the measure of the third angle. See Example 2. 147° 12' , 30° 19'

115

The measures of two angles of a triangle are given. Find the measure of the third angle. See Example 2. 29.6° , 49.7°

154

The measures of two angles of a triangle are given. Find the measure of the third angle. See Example 2. 17° 41' 13" , 96° 12' 10"

188

Concept Check Classify each triangle as acute, right, or obtuse. Also classify each as equilateral, isosceles, or scalene. See the discussion following Example 2.

126

Concept Check Classify each triangle as acute, right, or obtuse. Also classify each as equilateral, isosceles, or scalene. See the discussion following Example 2.

117

Convert each radian measure to degrees. See Examples 2(a) and 2(b). ―7π/20

159

Convert each radian measure to degrees. See Examples 2(a) and 2(b). 11π/30

106

Concept Check Classify each triangle as acute, right, or obtuse. Also classify each as equilateral, isosceles, or scalene. See the discussion following Example 2.

111

Convert each radian measure to degrees. See Examples 2(a) and 2(b). 15π

102

Find the unknown side lengths in each pair of similar triangles. See Example 4.

147

Solve each problem. See Example 5. Height of a Lighthouse The Biloxi lighthouse in the figure casts a shadow 28 m long at 7 A.M. At the same time, the shadow of the lighthouse keeper, who is 1.75 m tall, is 3.5 m long. How tall is the lighthouse?

122

Solve each problem. See Example 5. Height of a Building A house is 15 ft tall. Its shadow is 40 ft long at the same time that the shadow of a nearby building is 300 ft long. Find the height of the building.

109

Solve each problem. See Example 5. Height of a Carving of Lincoln Assume that Lincoln was 6 1/3 ft tall and his head was 3/4 ft long. Knowing that the carved head of Lincoln at Mt. Rushmore is 60 ft tall, find how tall his entire body would be if it were carved into the mountain.

141

In Exercises 65–66, an object moves in simple harmonic motion described by the given equation, where t is measured in seconds and d in centimeters. In each exercise, find: a. the maximum displacement b. the frequency c. the time required for one cycle. d = 20 cos π/4 t

174

In each figure, there are two similar triangles. Find the unknown measurement. Give approximations to the nearest tenth.

110

In Exercises 67–68, an object is attached to a coiled spring. In Exercise 67, the object is pulled down (negative direction from the rest position) and then released. In Exercise 68, the object is propelled downward from its rest position. Write an equation for the distance of the object from its rest position after t seconds.

196

Solve each problem. Solar Eclipse on Earth The sun has a diameter of about 865,000 mi with a maximum distance from Earth's surface of about 94,500,000 mi. The moon has a smaller diameter of 2159 mi. For a total solar eclipse to occur, the moon must pass between Earth and the sun. The moon must also be close enough to Earth for the moon's umbra (shadow) to reach the surface of Earth. (Data from Karttunen, H., P. Kröger, H. Oja, M. Putannen, and K. Donners, Editors, Fundamental Astronomy, Fourth Edition, Springer-Verlag.) a. Calculate the maximum distance, to the nearest thousand miles, that the moon can be from Earth and still have a total solar eclipse occur. (Hint: Use similar triangles.)

137

Solar Eclipse on Neptune (Refer to Exercise 69.) The sun's distance from Neptune is approximately 2,800,000,000 mi (2.8 billion mi). The largest moon of Neptune is Triton, with a diameter of approximately 1680 mi. (Data from The World Almanac and Book of Facts.) b. Triton is approximately 220,000 mi from Neptune. Is it possible for Triton to cause a total eclipse on Neptune?

143

Solar Eclipse on Mars (Refer to Exercise 69.) The sun's distance from the surface of Mars is approximately 142,000,000 mi. One of Mars' two moons, Phobos, has a maximum diameter of 17.4 mi. (Data from The World Almanac and Book of Facts.) b. Phobos is approximately 5800 mi from Mars. Is it possible for Phobos to cause a total eclipse on Mars?

109