AN66 Answers: Chapter 9 11. R x x x x x 2 1 4 5 3 ; ( ) ( )( ) ( )( ) = + − + − domain: x x x 5, 3 { } ≠ − ≠ Intercepts: 1 2 , 0 , ( ) − ( ) 4, 0 , 0, 4 15 ( ) No symmetry Vertical asymptotes: x x 5, 3 = − = Horizontal asymptote: y 2 = Intersects the horizontal asymptote, y 2, = at the point 26 11 , 2 ( ) y 10 x 10 (4, 0) 1 2 , 0 2 4 15 0, 26 11 , 2 12. 2.26 { } 13. 1{ } 14. (a) 5 4 { } − (b) 2{ } (c) 1 3 13 2 , 1 3 13 2 { } − − − + (d) x x 5 4 { } >− or 5 4 , ( ) − ∞ (e) x x 8 3 { } − ≤ ≤ or 8, 3 [ ] − (f) y 6 x 5 (0, 5) (21.25, 0) (g) y 15 x 10 (3, 0) (28, 0) (22.5, 230.25) (0, 224) CHAPTER 9 Polar Coordinates; Vectors 9.1 Assess Your Understanding (page 607) 7. pole; polar axis 8. θ θ r r cos; sin 9. b 10. d 11. T 12. F 13. A 15. C 17. B 19. A 21. 3, O P 2 P 2 23. O (22, 0) 25. O P 6 6, P 6 27. 22, O 3P 4 3P 4 29. O 2P 3 4, 2 2P 3 2 31. O P 32 P 3 21, 2 33. (22, 2P) O 2P 35. 2P 3 2P 3 5, O (a) π ( ) − 5, 4 3 (b) π ( ) −5, 5 3 (c) π ( ) 5, 8 3 37. (22, 3P) O 3P (a) π ( ) − 2, 2 (b) π ( ) −2, (c) π ( ) 2, 2 39. O P 2 1, P 2 (a) π ( ) − 1, 3 2 (b) π ( ) −1, 3 2 (c) π ( ) 1, 5 2 41. P 42 P 4 23, 2 O (a) π ( ) − 3, 5 4 (b) π ( ) −3, 7 4 (c) π ( ) 3, 11 4 43. ( ) 0, 3 45. ( ) −2, 0 47. ( ) −3 3, 3 49. ( ) − 2, 2 51. − ⎛ ⎝ ⎜⎜⎜ ⎞ ⎠ ⎟⎟ ⎟ 5 3 2 , 5 2 53. ( ) 2, 0 55. ( ) −2.57, 7.05 57. ( ) − − 4.98, 3.85 59. ( ) 3, 0 61. π ( ) 1, 63. π ( ) − 2, 4 65. π ( ) 10, 3 67. ( ) − 2.47, 1.02 69. ( ) 9.30, 0.47 71. = = r r 3 2 or 6 2 2 73. θ θ − = r r cos 4 sin 0 2 2 75. θ = r sin2 1 2 77. θ = r cos 4 79. ( ) + − = − + = x y x x y 0 or 1 2 1 4 2 2 2 2 81. + = + x y y x 2 2 2 83. + = x y 4 2 2 85. ( ) = + y x 8 2 2 87. (a) ( ) −10, 36 (b) ( ) ( ) ( ) ° + − ≈ ° − 2 349, 180 tan 18 5 37.36, 105.5 1 (c) ( ) − − 3, 35 (d) ( ) ( ) ( ) ° + ≈ ° − 1234, 180 tan 35 3 35.13, 265.1 1 89. (a) ( ) ( ) ° − ° 80, 25 ; 110, 5 (b) ( ) ( ) − 72.50, 33.81 ; 109.58, 9.59 (c) 342.5 mph 94. { } 19 15 95. 2 or 0 positive real zeros; 1 negative real zero 96. ( ) − 5 4 , 9 2 97. ( ) − 0, 11 98. − i 13 18 99. π π π π { } 12 , 5 12 , 13 12 , 17 12 100. = ° ≈ ≈ C a b 78 , 9.27, 6.15 101. + 6 2 4 or ( ) + 2 1 3 4 102. ( ) − e x x 3 2 5 x3 3 103. ( ) ( ) ( ) = = − = − + = − + x x x x x x x x x x x x x sin sin sin sin 1 cos sin 1 2 cos cos sin 2 cos sin cos sin 5 2 2 2 2 2 4 2 4 9.2 Assess Your Understanding (page 624) 7. polar equation 8. F 9. θ− 10. π θ − 11. 2n; n 12. T 13. c 14. b 15. + = x y 16; 2 2 circle, radius 4, center at pole 3P 4 U 5 5P 4 U 5 3P 2 U 5 7P 4 U 5 P 2 U 5 P 4 U 5 y x 1 2 3 4 5 U 5 P U 5 0 17. = y x3 ; line through pole, making an angle of π 3 with polar axis 3P 4 U 5 5P 4 U 5 3P 2 U 5 7P 4 U 5 P 2 U 5 P 4 U 5 P 3 U 5 y x 1 2 3 4 5 U 5 P U 5 0 19. = y 4; horizontal line 4 units above the pole 3P 4 U 5 5P 4 U 5 3P 2 U 5 7P 4 U 5 P 2 U 5 P 4 U 5 y x 1 2 3 4 5 U 5 P U 5 0
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