Exercises 10.1, page 302

  1. 1. y = 3 cos x

    A curve oscillates about y = 0 with amplitude 3, period 2 pi, and maximum (0, 3).
  2. 3. 0,  − 0.7 ,   − 1 ,   − 0.7 ,  0, 0.7, 1, 0.7, 0,  − 0.7 ,   − 1 ,   − 0.7 ,  0, 0.7, 1, 0.7, 0

    A curve oscillates about y = 0 with amplitude 1, local maximum (pi over 2, 1), and period 2 pi.
  3. 5. 3, 2.1, 0,  − 2.1 ,   − 3 ,   − 2.1 ,  0, 2.1, 3, 2.1, 0,  − 2.1 ,   − 3 ,   − 2.1 ,  0, 2.1, 3

    A curve oscillates about y = 0 with amplitude 3, local maximum (pi, 3), and period 2 pi.
  4. 7. Amplitude  = 3

    A curve oscillates about y = 0 with amplitude 3, local maximum (pi over 2, 3), and period 2 pi.
  5. 9. Amplitude  = 52

    A graph of a curve that oscillates about y = 0 with amplitude 5 over 2, local maximum (pi over 2, 5 over 2), and period 2 pi.
  6. 11. Amplitude  = 200

    A graph of a curve that oscillates about y = 0 with amplitude 200, local maximum (0, 200), and period 2 pi.
  7. 13. Amplitude  = 0.8

    A graph of a curve that oscillates about y = 0 with amplitude 0.8, local maximum (0, 0.8), and period 2 pi.
  8. 15. Amplitude  = 1

    A graph of a curve that oscillates about y = 0 with amplitude 1, local maximum (3 pi over 2, 1), and period 2 pi.
  9. 17. Amplitude  = 1500

    A graph of a curve that oscillates about y = 0 with amplitude 1500, local maximum (3 pi over 2, 1500), and period 2 pi.
  10. 19. Amplitude  = 4

    A graph of a curve that oscillates about y = 0 with amplitude 4, local maximum (pi, 4), and period 2 pi.
  11. 21. Amplitude  = 50

    A graph of a curve that oscillates about y = 0 with amplitude 50, local maximum (pi, 50), and period 2 pi.
  12. 23. 0, 0.84, 0.91, 0.14,  − 0.76 ,   − 0.96 ,   − 0.28 ,  0.66

    A graph of a curve that oscillates about y = 0 with amplitude 1, local maximum (1.6, 1), and period 6.2. All data are approximate.
  13. 25. − 12 ,   − 6.48 ,  4.99 ,  11.88 ,  7.84 ,   − 3.40 ,   − 11.52 ,   − 9.05

    A graph of a curve that oscillates about y = 0 with amplitude 12, local maximum (3, 12), and period 6.
  14. 27. y =  − 2 sin x

    A graph of a curve that oscillates about y = 0 with amplitude 2, local maximum (3 pi over 2, 2), and period 2 pi.
  15. 29.

    A graph of a curve that oscillates about y = 0 with amplitude 32, local maximum (pi, 32), and period 2 pi.
  16. 31.

    A calculator graph of a curve that oscillates about y = 0 with amplitude 0.05, local maximum (4.5, 0.05), and period 6. All data are approximate.
  17. 33. y = 4 sin x

  18. 35. y =  − 1.5 cos x

  19. 37. y =  − 2.50 sin x

  20. 39. y =  − 2.50 cos x

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