1. Measuring Angles

Convert each radian measure to degrees.

5π/4

167

Convert each radian measure to degrees.

8π/3

125

Convert each radian measure to degrees.

-11π/18

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

39°

137

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

42.5°

106

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

139° 10'

139

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

174° 50'

124

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

64.29°

133

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

85.04°

143

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

56° 25'

108

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

122° 37'

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

-47.69°

129

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

2

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

5

132

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

3.06

131

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

0.3417

125

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

9.84763

116

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

-5.01095

105

Find each exact function value. See Example 3.

sin π/3

Find each exact function value. See Example 3.

tan π/4

127

Find each exact function value. See Example 3.

sec π/6

132

Find each exact function value. See Example 3.

sin π/2

138

Open Question

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

[0, 2π) ; sin s = -√3/ 2

174

Find each exact function value. See Example 3.

tan 5π/3

138

Find each exact function value. See Example 3.

sin 5π/6

Find each exact function value. See Example 3.

cos 3π

143

Find each exact function value. See Example 3.

sin (-8π/ 3)

145

Find each exact function value. See Example 3.

sin (-7π/ 6)

125

Find each exact function value. See Example 3.

tan (-14π/ 3)

114

Work each problem.

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

3

147

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

193

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

163

Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b).

60°

146

Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b).

30°

115

Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b).

90°

113

Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b).

150°

Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b).

- 300°

Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b).

- 315°

Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b).

450°

Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b).

1800°

108

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

285

Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b).

3600°

145

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

252

Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b).

- 900°

113

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

215

Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b).

- 1800°

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

320

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

π/3

134

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

7π/4

112

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

11π/6

135

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

- π/6

123

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

- 8π/5

107

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)

213

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

11π/15

111

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)

265

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

- 7π/20

116

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

11π/30

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

15π

117

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

149

Work each problem.

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

4

117

Work each problem.

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

-2

127

Work each problem.

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

7

136

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

139

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

45°

123

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

175°

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

800°

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

53

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

66

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

60

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

62

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

61

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

78

62

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

78

90

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

74

69

67

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

63

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.)

83

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

69

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

97

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

80

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

127

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

78

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

77

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

77

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?

84

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

63

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

77

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"

85

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

65

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

63

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

72

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

55

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

65

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

58

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

76

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?

57

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.

60

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.

68

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

113

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

57

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.

124

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.)

56

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?

70

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?

61