Name: Trigonometry
Author: Lial
ISBN: 9780136552161

Ch. 3 - Radian Measure and The Unit Circle

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Lial 12th Edition

Ch. 3 - Radian Measure and The Unit Circle

3.2 Applications of Radian Measure

Problem 23

Distance between Cities Find the distance in kilometers between each pair of cities, assuming they lie on the same north-south line. Assume the radius of Earth is 6400 km. See Example 2. Panama City, Panama, 9° N, and Pittsburgh, Pennsylvania, 40° N

Problem 24

Distance between Cities Find the distance in kilometers between each pair of cities, assuming they lie on the same north-south line. Assume the radius of Earth is 6400 km. See Example 2.

Farmersville, California, 36° N, and Penticton, British Columbia, 49° N

Problem 25

Distance between Cities Find the distance in kilometers between each pair of cities, assuming they lie on the same north-south line. Assume the radius of Earth is 6400 km. See Example 2.

New York City, New York, 41° N, and Lima, Peru, 12° S

Problem 26

Distance between Cities Find the distance in kilometers between each pair of cities, assuming they lie on the same north-south line. Assume the radius of Earth is 6400 km. See Example 2.

Halifax, Nova Scotia , 45° N, and Buenos Aires, Argentina, 34° S

Problem 41

Distance Traveled by a Minute Hand Suppose the tip of the minute hand of a clock is 3 in. from the center of the clock. For each duration, determine the distance traveled by the tip of the minute hand. Leave answers as multiples of π . 30 min

Problem 43

Problem 49

Find the area of a sector of a circle having radius r and central angle θ. Express answers to the nearest tenth. See Example 5. r = 29.2 m, θ = 5π/6 radians

Problem 51

Find the area of a sector of a circle having radius r and central angle θ. Express answers to the nearest tenth. See Example 5.

r = 30.0 ft, θ = π/2 radians

Problem 53

Find the area of a sector of a circle having radius r and central angle θ. Express answers to the nearest tenth. See Example 5.

r = 12.7 cm, θ = 81°

Problem 55

Find the area of a sector of a circle having radius r and central angle θ. Express answers to the nearest tenth. See Example 5.

r = 40.0 mi, θ = 135°

Problem 57

Work each problem. See Example 5. Angle Measure Find the measure (in radians) of a central angle of a sector of area 16 in² a circle of radius 3.0 in.

Problem 59

Work each problem. See Example 5. Irrigation Area A center-pivot irrigation system provides water to a sector-shaped field as shown in the figure. Find the area of the field if θ = 40.0° and r = 152 yd.

Problem 61

Work each problem. See Example 5. Arc Length A circular sector has an area of 50 in² . The radius of the circle is 5 in. What is the arc length of the sector?

3.3 The Unit Circle and Circular Functions

Problem 7

Each figure shows an angle θ in standard position with its terminal side intersecting the unit circle. Evaluate the six circular function values of θ.

Problem 9

Each figure shows an angle θ in standard position with its terminal side intersecting the unit circle. Evaluate the six circular function values of θ.

Problem 11

Find the exact values of (a) sin s, (b) cos s, and (c) tan s for each real number s. See Example 1.

s = π/2

Problem 13

Find the exact values of (a) sin s, (b) cos s, and (c) tan s for each real number s. See Example 1.

s = 2π

Problem 15

Find the exact values of (a) sin s, (b) cos s, and (c) tan s for each real number s. See Example 1.

s = ―π