Solutions for Angles

Solutions to Try Its

1.
Graph of a 240 degree angle.

2. [latex]\frac{3\pi }{2}[/latex]

3. −135°

4. [latex]\frac{7\pi }{10}[/latex]

5. [latex]\alpha =150^\circ [/latex]

6. [latex]\beta =60^\circ [/latex]

7. [latex]\frac{7\pi }{6}[/latex]

8. [latex]\frac{215\pi }{18}=37.525\text{ units}[/latex]

9. 1.88

10. [latex]\frac{-3\pi }{2}[/latex] rad/s

11. 1655 kilometers per hour

Solutions to Odd-Numbered Exercises

1.
Graph of a circle with an angle inscribed, showing the initial side, terminal side, and vertex.

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.
Graph of a circle with an angle inscribed.

9.
Graph of a circle with an angle inscribed.

11.
Graph of a circle with an angle inscribed.

13.
Graph of a circle with an angle inscribed.

15.
Graph of a circle with an angle inscribed.

17. 240°
Graph of a circle with an angle inscribed.

19. [latex]\frac{4\pi }{3}[/latex]
Graph of a circle showing the equivalence of two angles.

21. [latex]\frac{2\pi }{3}[/latex]
Graph of a circle showing the equivalence of two angles.

23. [latex]\frac{7\pi }{2}\approx 11.00{\text{ in}}^{2}[/latex]

25. [latex]\frac{81\pi }{20}\approx 12.72{\text{ cm}}^{2}[/latex]

27. 20°

29. 60°

31. −75°

33. [latex]\frac{\pi }{2}[/latex] radians

35. [latex]-3\pi [/latex] radians

37. [latex]\pi [/latex] radians

39. [latex]\frac{5\pi }{6}[/latex] radians

41. [latex]\frac{5.02\pi }{3}\approx 5.26[/latex] miles

43. [latex]\frac{25\pi }{9}\approx 8.73[/latex] centimeters

45. [latex]\frac{21\pi }{10}\approx 6.60[/latex] meters

47. 104.7198 cm2

49. 0.7697 in2

51. 250°

53. 320°

55. [latex]\frac{4\pi }{3}[/latex]

57. [latex]\frac{8\pi }{9}[/latex]

59. 1320 rad 210.085 RPM

61. 7 in./s, 4.77 RPM, 28.65 deg/s

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

65. [latex]5.76[/latex] miles

67. [latex]120^\circ [/latex]

69. 794 miles per hour

71. 2,234 miles per hour

73. 11.5 inches