B Apply

34. Space A geostationary satellite is positioned 35,800 km above Earth's surface. It takes 24 h to complete one orbit. The radius of Earth is about 6400 km. See Problem 4.

    1. What distance does the satellite travel in 1 h? 3 h? 2.5 h? 25 h?
    2. Reasoning After how many hours has the satellite traveled 200,000 km?
35. Think About a Plan Suppose a windshield wiper arm has a length of 22 in. and rotates through an angle of 110°. What distance does the tip of the wiper travel as it moves once across the windshield?
    • Which formula can help you answer this question?
    • Do you need to convert between degrees and radians?
36. Geography The 24 lines of longitude that approximate the 24 standard time zones are equally spaced around the equator.
    1. Suppose you use 24 central angles to divide a circle into 24 equal arcs. Express the measure of each angle in degrees and in radians.
    2. The radius of the equator is about 3960 mi. About how wide is each time zone at the equator?
    3. The radius of the Arctic Circle is about 1580 mi. About how wide is each time zone at the Arctic Circle?

Determine the quadrant or axis where the terminal side of each angle lies.

37. 4 π 3  radians fraction 4 pi , over 3 end fraction . radians
38. − 5 π 4  radians negative , fraction 5 pi , over 4 end fraction . radians
39. − π  radians negative pi , radians
40. 6 π 5  radians fraction 6 pi , over 5 end fraction . radians

Draw an angle in standard position with each given measure. Then find the values of the cosine and sine of the angle.

41. 7 π 4  radians fraction 7 pi , over 4 end fraction . radians
42. − 2 π 3  radians negative , fraction 2 pi , over 3 end fraction . radians
43. 5 π 2  radians fraction 5 pi , over 2 end fraction . radians
44. 7 π 6  radians fraction 7 pi , over 6 end fraction . radians
45. Writing Two angles are measured in radians. Explain how to tell whether the angles are coterminal without rewriting their measures in degrees.
46. Open-Ended Draw an angle in standard position. Draw a circle with its center at the vertex of the angle. Find the measure of the angle in radians and degrees.
47. Transportation Suppose the radius of a bicycle wheel is 13 in. (measured to the outside of the tire). Find the number of radians through which a point on the tire turns when the bicycle has moved forward a distance of 12 ft.

48. Error Analysis A student wanted to rewrite 9 π 4  radians fraction 9 pi , over 4 end fraction . radians  in degrees. The screen shows her calculation. What error did the student make?

    

49. Music A CD with diameter 12 cm spins in a CD player. Calculate how much farther a point on the outside edge of the CD travels in one revolution than a point 1 cm closer to the center of the CD.
50. Geography Assume that Earth is a sphere with radius 3960 miles. A town is at latitude 32° N. Find the distance in miles from the town to the North Pole. (Hint: Latitude is measured north and south from the equator.)

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