A-32 Answers to Selected Exercises 19. -1; 0; undefined; 0; undefined; -1 20. 135°; 225° 21. 240°; 300° 22. 45°; 225° 23. Take the reciprocal of tan u to obtain cot u = 0.59600119. 24. (a) 0.979399 (b) -1.905608 (c) 1.936213 25. 16.166641° [5.4] 26. B = 31° 30′ ; c = 877 ; b = 458 27. 67.1°, or 67° 10′ 28. 15.5 ft 29. 8800 ft 30. 72 nautical mi 31. 92 km 32. 448 m 31. 60 61 ; 11 61 ; 60 11 ; 11 60 ; 61 11 ; 61 60 33. - 23 2 ; 1 2 ; - 23 ; - 23 3 ; 2; - 2 23 3 35. - 1 2 ; 23 2 ; - 23 3 ; - 23 ; 2 23 3 ; -2 37. 120°; 240° 39. 150°; 210° 41. - 22 2 ; - 2 2 ; 1 43. - 1.356342 45. 1.021034 47. 0.208344 49. 55.673870° 51. 12.733938° 53. 63.008286° 55. 47°; 133° 57. No, this will result in an angle having tangent equal to 25. The function tan-1 is not the reciprocal of the tangent (cotangent) but is, rather, the inverse tangent function. To find cot 25°, the student must find the reciprocal of tan 25°. 59. B = 31° 30′ ; a = 638 ; b = 391 61. B = 50.28°; a = 32.38 m; c = 50.66 m 63. 73.7 ft 65. 18.75 cm 67. 1200 m 69. 140 mi Chapter 5Test [5.1] 1. 23°; 113° 2. 145°; 35° 3. 20°; 70° 4. 74.31° 5. 45° 12′ 09″ 6. (a) 30° (b) 280° (c) 90° 7. 2700° [5.2] 8. 0 x y (2, –7) U 2 –7 sin u = - 7253 53 ; cos u = 2253 53 ; tan u = - 7 2 ; cot u = - 2 7 ; sec u = 253 2 ; csc u = - 253 7 9. 0 x y (0, –2) U 2 sin u = -1; cos u = 0; tan u is undefined; cot u = 0; sec u is undefined; csc u = -1 10. 0 x y (–4, –3) U –3 –4 3x – 4y = 0, x ≤ 0 sin u = - 3 5 ; cos u = - 4 5 ; tan u = 3 4 ; cot u = 4 3 ; sec u = - 5 4 ; csc u = - 5 3 11. row 1: 1, 0, undefined, 0, undefined, 1; row 2: 0, 1, 0, undefined, 1, undefined; row 3: -1, 0, undefined, 0, undefined, -1 12. cosecant and cotangent 13. (a) I (b) III, IV (c) III 14. cos u = - 2210 7 ; tan u = - 3210 20 ; cot u = - 2210 3 ; sec u = - 7210 20 ; csc u = 7 3 [5.3] 15. sin A = 12 13 ; cos A = 5 13 ; tan A = 12 5 ; cot A = 5 12 ; sec A = 13 5 ; csc A = 13 12 16. x = 4 ; y = 4 23 ; z = 422 ; w = 8 In Exercises 17–19, we give, in order, sine, cosine, tangent, cotangent, secant, and cosecant. 17. - 23 2 ; - 1 2 ; 23 ; 23 3 ; -2; - 223 3 18. - 22 2 ; - 22 2 ; 1; 1; - 22 ; - 2 Chapter 6The Circular Functions and Their Graphs 6.1 Exercises 1. radius 3. p 180 5. 2p 7. 2 9. 1 11. p 3 13. p 2 15. 5p 6 17. - 5p 3 19. 5p 2 21. 10p 23. 0 25. -5p 27. 60° 29. 315° 31. 330° 33. -30° 35. 126° 37. -48° 39. 153° 41. -900° 43. 0.681 45. 0.742 47. 2.429 49. 1.122 51. 0.985 53. -0.832 55. 114° 35′ 57. 99° 42′ 59. 19° 35′ 61. -287° 06′ 63. In the expression “sin 30,” 30 means 30 radians; sin 30° = 1 2 , and sin 30 ≈ -0.9880. 65. We begin the answers with the blank next to 30°, and then proceed counterclockwise from there: p 6 ; 45; p 3 ; 120; 135; 5p 6 ; p; 7p 6 ; 5p 4 ; 240; 300; 7p 4 ; 11p 6 . 67. 25.8 cm 69. 3.61 ft 71. 5.05 m 73. 55.3 in. 75. 3500 km 77. 5900 km 79. 44° N 81. 156° 83. 38.5° 85. 18.7 cm 87. (a) 11.6 in. (b) 37° 05′ 89. 146 in. 91. 86 ft 93. 3p in. 95. 27p in. 97. 0.20 km 99. 840 ft 101. 1116.1 m2 103. 706.9 ft2 105. 114.0 cm2 107. 1885.0 mi2 109. 3.6 111. 8060 yd2 113. 20 in. 115. (a) 13 1 3 °; 2p 27 (b) 478 ft (c) 17.7 ft (d) 672 ft2 117. (a) 140 ft (b) 102 ft (c) 622 ft2 119. 1900 yd2 121. 13.9 ft2 6.2 Exercises 1. Counterclockwise from 0 radians, the coordinates are 11, 02, Q 23 2 , 1 2R , Q 22 2 , 22 2 R , Q 1 2 , 23 2 R , and 10, 12. 3. 22 2 5. 1 7. linear speed (or linear velocity) 9. 2p 11. 2p 13. (a) 1 (b) 0 (c) undefined 15. (a) 0 (b) 1 (c) 0 17. (a) 0 (b) -1 (c) 0 19. - 1 2 21. -1 23. -2 25. - 1 2 27. 22 2 29. 23 2 31. 223 3 33. - 23 3 35. 0.5736 37. 0.4068 39. 1.2065 41. 14.3338 43. -1.0460 45. -3.8665 47. 0.7 49. 0.9 51. -0.6 53. 2.3 or 4.0 55. 0.8 or 2.4 57. negative 59. negative 61. positive 63. 0.2095 65. 1.4426 67. 0.3887 69. 5p 6 71. 4p 3 73. 7p 4 75. 4p 3 , 5p 3 77. p 4 , 3p 4 , 5p 4 , 7p 4 79. - 11p 6 , - 7p 6 , - 5p 6 , - p 6 , p 6 , 5p 6 81. (a) p 2 radians (b) 10p cm (c) 5p 3 cm per sec 83. (a) 3p radians (b) 24p in. (c) 8p 3 in. per min 85. 2p radians
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