AN46 Answers: Chapter 6 21. −1 23. 0 25. −1 27. 0 29. −1 31. ( ) + 1 2 2 1 33. 2 35. 1 2 37. 6 39. 4 41. 0 43. + 2 2 4 3 3 45. 1 47. π π π π = = − = − = sin 2 3 3 2 ; cos 2 3 1 2 ; tan 2 3 3; csc 2 3 2 3 3 ; π π = − = − sec 2 3 2; cot 2 3 3 3 49. ° = − ° = − ° = ° = − ° = − ° = sin210 1 2 ; cos210 3 2 ; tan210 3 3 ; csc210 2; sec210 2 3 3 ; cot210 3 51. π π π π π π = = − = − = = − = − sin 3 4 2 2 ; cos 3 4 2 2 ; tan 3 4 1; csc 3 4 2; sec 3 4 2; cot 3 4 1 53. π π π π π = = − = − = = − sin 8 3 3 2 ; cos 8 3 1 2 ; tan 8 3 3; csc 8 3 2 3 3 ; sec 8 3 2; π = − cot 8 3 3 3 55. ° = ° = ° = ° = ° = ° = sin405 2 2 ; cos405 2 2 ; tan405 1; csc405 2; sec405 2; cot405 1 57. π π π π π π ( ) ( ) ( ) ( ) ( ) ( ) − = − − = − = − − = − − = − = − sin 6 1 2 ; cos 6 3 2 ; tan 6 3 3 ; csc 6 2; sec 6 2 3 3 ; cot 6 3 59. ( ) ( ) ( ) ( ) ( ) ( ) − ° = − − ° = − −°= −°=− −°=− −°= sin 135 2 2 ; cos 135 2 2 ; tan 135 1; csc 135 2; sec 135 2; cot 135 1 61. π π π = = sin 5 2 1; cos 5 2 0; tan 5 2 is undefined; π π = csc 5 2 1; sec 5 2 is undefined; π = cot 5 2 0 63. π π π π π π ( ) ( ) ( ) ( ) ( ) ( ) − = − − = − − = − = − − = − − = sin 14 3 3 2 ; cos 14 3 1 2 ; tan 14 3 3; csc 14 3 2 3 3 ; sec 14 3 2; cot 14 3 3 3 65. 0.47 67. 1.07 69. 0.32 71. 3.73 73. 0.84 75. 0.02 77. θ θ θ θ θ θ = = − = − = = − = − sin 4 5 ; cos 3 5 ; tan 4 3 ; csc 5 4 ; sec 5 3 ; cot 3 4 79. θ θ θ θ θ θ = − = = − = − = = − sin 3 13 13 ; cos 2 13 13 ; tan 3 2 ; csc 13 3 ; sec 13 2 ; cot 2 3 81. θ θ θ θ θ θ = − = − = = − = − = sin 2 2 ; cos 2 2 ; tan 1; csc 2; sec 2; cot 1 83. θ = sin 3 5 ; θ θ θ θ θ = = = = = cos 4 5 ; tan 3 4 ; csc 5 3 ; sec 5 4 ; cot 4 3 85. 0 87. 0 89. −0.1 91. 3 93. 5 95. 3 2 97. 1 2 99. 3 4 101. 3 2 103. 3 105. − 3 2 107. +1 3 2 109. − 1 2 111. 3 2 113. 2 4 115. (a) π⎛ ⎝ ⎜⎜⎜ ⎞ ⎠ ⎟⎟ ⎟ 2 2 ; 4 , 2 2 (b) π ⎛ ⎝ ⎜⎜⎜ ⎞ ⎠ ⎟⎟ ⎟ 2 2 , 4 (c) π( ) − 4 , 2 117. Answers may vary. One set of possible answers is π π π π π − − 11 3 , 5 3 , 3 , 7 3 , 13 3 . 119. θ 0.5 0.4 0.2 0.1 0.01 0.001 0.0001 0.00001 sinθ 0.4794 0.3894 0.1987 0.0998 0.0100 0.0010 0.0001 0.00001 sinθ θ 0.9589 0.9735 0.9933 0.9983 1.0000 1.0000 1.0000 1.0000 θ θ sin approaches 1 as θ approaches 0. 121. ≈ ≈ R H 310.56 ft; 77.64 ft 123. ≈ ≈ R H 19,541.95 m; 2278.14 m 125. (a) 1.20 sec (b) 1.12 sec (c) 1.20 sec 127. (a) 1.9 hr; 0.57 hr (b) 1.69 hr; 0.75 hr (c) 1.63 hr; 0.86 hr (d) 1.67 hr; tan ° 90 is undefined 129. 15.4 ft 131. 71 ft 133. (a) 466.9 ft, 587.7 ft, 612.0 ft (b) θ θ ( ) ( ) ≈ ° ≈ ° 0.678 38.8 or 1.364 78.2 (c) θ ( ) ≈ ° 0.986 56.5 ; this is larger than the angle needed to get the maximum range. 135. (a) 16.56 ft (b) 45 0 20 90 (c) ° 67.5 137. (a) values estimated to the nearest tenth: ≈ ≈ ≈ ≈ ≈ sin1 0.8; cos1 0.5; tan1 1.6; csc1 1.3; sec1 2.0; ≈ cot1 0.6; actual values to the nearest tenth: ≈ ≈ sin1 0.8; cos1 0.5; ≈ tan1 1.6; ≈ ≈ ≈ csc 1 1.2; sec1 1.9; cot1 0.6 (b) values estimated to the nearest tenth: ≈ − ≈ sin5.1 0.9; cos5.1 0.4; ≈ − ≈ − ≈ ≈ − tan5.1 2.3; csc5.1 1.1; sec5.1 2.5; cot5.1 0.4; actual values to the nearest tenth: ≈ − ≈ sin5.1 0.9; cos5.1 0.4; ≈ − tan5.1 2.4; ≈ − ≈ ≈ − csc5.1 1.1; sec5.1 2.6; cot5.1 0.4 139. = − y 4 3 7 141. − 12 13 146. { } > − x x 2 5 or ( ) − ∞ 2 5 , 147. − − i 4 3 , 5 148. = R 134 149. π 81 ft2 150. ±7 157 6 151. ( ) = f x x 1 2 152. [ ] −3, 2 153. [ ) − − 5, 4 154. ( ) − 6, 2 155. + x x 4 4 4 2 6.3 Assess Your Understanding (page 423) 5. π π 2 ; 6. All real numbers except odd multiples of π 2 7. b 8. a 9. 1 10. F 11. 2 2 13. 1 15. 1 17. 3 19. 2 2 21. 0 23. 2 25. 3 3 27. II 29. IV 31. IV 33. II 35. θ θ θ θ = − = − = = − tan 3 4 ; cot 4 3 ; sec 5 4 ; csc 5 3 37. θ θ θ = = = tan 2; cot 1 2 ; sec 5; θ = csc 5 2 39. θ θ θ θ = = = = tan 3 3 ; cot 3; sec 2 3 3 ; csc 2 41. θ θ θ θ = − = − = = − tan 2 4 ; cot 2 2; sec 3 2 4 ; csc 3 43. θ θ θ θ θ = − = − = = − = − cos 5 13 ; tan 12 5 ; csc 13 12 ; sec 13 5 ; cot 5 12 45. θ θ θ θ θ = − = = − = − = sin 3 5 ; tan 3 4 ; csc 5 3 ; sec 5 4 ; cot 4 3
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