SECTION 6.4 Graphs of the Sine and Cosine Functions 439 43. ( ) = y x 2sin 1 2 44. ( ) = y x 2cos 1 4 45. ( ) = − y x 1 2 cos 2 46. ( ) = − y x 4sin 1 8 47. = + y x 2 sin 3 48. = + y x 3cos 2 49. π( ) = − y x 5cos 3 50. π( ) = − y x 4sin 2 2 51. π( ) = − + y x 6sin 3 4 52. π( ) = − + y x 3cos 4 2 53. ( ) = − y x 5 3sin 2 54. ( ) = − y x 2 4cos 3 55. π ( ) = − y x 5 3 sin 2 3 56. π ( ) = − y x 9 5 cos 3 2 57. π( ) = − + y x 3 2 cos 4 1 2 58. π( ) = − + y x 1 2 sin 8 3 2 In Problems 59–62, write the equation of a sine function that has the given characteristics. 59. Amplitude: 3 Period: π 60. Amplitude: 2 Period: π4 61. Amplitude: 3 Period: 2 62. Amplitude: 4 Period: 1 In Problems 63–76, find an equation for each graph. 63. x y 24 22 2 4 6 5 8 10 25 64. x y 24p 22p 6p 2p 10p 24 4 65. x y 22p 2p 4p 23 3 66. x y 22 21 3 1 2 4 5 22 2 67. y 5 – 4 1 – 2 1 – 4 1 – 2 1 x 2 3 – 4 3 – 4 2 68. y 3 – 2 5 – 2 1 – 2 1 – 2 1 2 21 x 2 5 – 2 5 – 2 2 69. y 1 21 2p ––– 3 4p ––– 3 2p ––– 3 2 x 70. y p 2p p 2p 2p x 71. x y 2 1 3 –– 4 3 –– 4 3 –– 2 2 72. x y 2 2p –––– 3 2p –––– 3 4p –––– 3 1 –– 22 3 –– 22
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