Solutions to Try Its

1.

2. $\frac{3\pi }{2}$

3. −135°

4. $\frac{7\pi }{10}$

5. $\alpha =150^\circ$

6. $\beta =60^\circ$

7. $\frac{7\pi }{6}$

8. $\frac{215\pi }{18}=37.525\text{ units}$

9. 1.88

10. $\frac{-3\pi }{2}$ rad/s

11. 1655 kilometers per hour

Solutions to Odd-Numbered Exercises

1.

3. Whether the angle is positive or negative determines the direction. A positive angle is drawn in the counterclockwise direction, and a negative angle is drawn in the clockwise direction.

5. Linear speed is a measurement found by calculating distance of an arc compared to time. Angular speed is a measurement found by calculating the angle of an arc compared to time.

7.

9.

11.

13.

15.

17. 240°

19. $\frac{4\pi }{3}$

21. $\frac{2\pi }{3}$

23. $\frac{7\pi }{2}\approx 11.00{\text{ in}}^{2}$

25. $\frac{81\pi }{20}\approx 12.72{\text{ cm}}^{2}$

27. 20°

29. 60°

31. −75°

33. $\frac{\pi }{2}$ radians

35. $-3\pi$ radians

37. $\pi$ radians

39. $\frac{5\pi }{6}$ radians

41. $\frac{5.02\pi }{3}\approx 5.26$ miles

43. $\frac{25\pi }{9}\approx 8.73$ centimeters

45. $\frac{21\pi }{10}\approx 6.60$ meters

47. 104.7198 cm2

49. 0.7697 in2

51. 250°

53. 320°

55. $\frac{4\pi }{3}$

57. $\frac{8\pi }{9}$

59. 1320 rad 210.085 RPM

61. 7 in./s, 4.77 RPM, 28.65 deg/s

63. $1,809,557.37\text{ mm/min}=30.16\text{ m/s}$

65. $5.76$ miles

67. $120^\circ$

69. 794 miles per hour

71. 2,234 miles per hour

73. 11.5 inches