Exercises 20.3, page 549

  1. 1.  − 3

  2. 3.  − 2425

  3. 5.

    sin 60 °  = sin 2(30 ° ) = 2 sin 30 °  cos 30 °  = 2(12)(123) = 123

  4. 7. tan 120 °  = 2 tan 60 ° 1 − tan2 60 °  = 231 − (3)2 =  − 3

  5. 9. sin 100 °  = 2 sin 50 ° cos 50 °  = 0.9848

  6. 11. cos 96 °  = cos2 48 °  − sin2 48 °  =  − 0.1045285

  7. 13.

    tan2π7 = 2 tanπ71 − tan2π7 = 1.254

  8. 15. 2425

  9. 17.  − 3

  10. 19. 3 sin 10x

  11. 21. cos 8x

  12. 23. cos x

  13. 25.  − 4 cos 4x

  14. 27. 2 sin 3θ

  15. 29. 2

  16. 31. cos2 α − (1 − cos2 α)

  17. 33. cos x − (sin x / cos x)sin x1 / cos x = cos2 x − sin2 x

  18. 35. 2 sin θ cos θ1 + 2 cos2 θ − 1 = sin θcos θ

  19. 37. 1 − (1 − 2 sin2 2θ) = 2csc2 θ

  20. 39. ln 1 − cos 2x1 + cos 2x = ln 2 sin2 x2 cos2 x = ln tan2 x

  21. 41.

    The calculator graph of curves that are periodic about the x-axis. One curve rises from x = negative 1 with decreasing steepness, inflects at (0, 0), then approaches x = 1.
  22. 43.

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