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Study Guides > Precalculus II

Solutions for Angles

Solutions to Try Its

1. Graph of a 240 degree angle. 2. 3π2\frac{3\pi }{2} 3. −135° 4. 7π10\frac{7\pi }{10} 5. α=150∘\alpha =150^\circ 6. β=60∘\beta =60^\circ 7. 7π6\frac{7\pi }{6} 8. 215π18=37.525 units\frac{215\pi }{18}=37.525\text{ units} 9. 1.88 10. −3π2\frac{-3\pi }{2} 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. 4π3\frac{4\pi }{3} Graph of a circle showing the equivalence of two angles. 21. 2π3\frac{2\pi }{3} Graph of a circle showing the equivalence of two angles. 23. 7π2≈11.00 in2\frac{7\pi }{2}\approx 11.00{\text{ in}}^{2} 25. 81π20≈12.72 cm2\frac{81\pi }{20}\approx 12.72{\text{ cm}}^{2} 27. 20° 29. 60° 31. −75° 33. π2\frac{\pi }{2} radians 35. −3π-3\pi radians 37. π\pi radians 39. 5π6\frac{5\pi }{6} radians 41. 5.02π3≈5.26\frac{5.02\pi }{3}\approx 5.26 miles 43. 25π9≈8.73\frac{25\pi }{9}\approx 8.73 centimeters 45. 21π10≈6.60\frac{21\pi }{10}\approx 6.60 meters 47. 104.7198 cm2 49. 0.7697 in2 51. 250° 53. 320° 55. 4π3\frac{4\pi }{3} 57. 8π9\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 mm/min=30.16 m/s1,809,557.37\text{ mm/min}=30.16\text{ m/s} 65. 5.765.76 miles 67. 120∘120^\circ 69. 794 miles per hour 71. 2,234 miles per hour 73. 11.5 inches

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