629 6.3 Graphs of the Sine and Cosine Functions 3. The graph of the sine function crosses the x-axis for all numbers of the form , where n is an integer. 4. The domain of both the sine and cosine functions (in interval form) is , and the range is . 5. The least positive number x for which cos x = 0 is . 6. On the interval 3p, 2p4, the function values of the cosine function increase from to . Concept Check Match each function with its graph in choices A – F. 7. y = -sin x 8. y = -cos x 9. y = sin 2x 10. y = cos 2x 11. y = 2 sin x 12. y = 2 cos x A. x 0 p p 2 y –1 1 D. x 0 2p p y –1 1 B. x y –1 1 0 p p 2 E. x 0 2p p y –1 1 C. x y –2 2 0 2p p F. x y –2 0 2 2p p Graph each function over the interval 3-2p, 2p4. Give the amplitude. See Example 1. 13. y = 2 cos x 14. y = 3 sin x 15. y = 2 3 sin x 16. y = 3 4 cos x 17. y = -cos x 18. y = -sin x 19. y = -2 sin x 20. y = -3 cos x 21. y = sin1-x2 22. Concept Check In Exercise 21, why is the graph the same as that of y = -sin x? Graph each function over a two-period interval. Give the period and amplitude. See Examples 2 – 5. 23. y = sin 1 2 x 24. y = sin 2 3 x 25. y = cos 3 4 x 26. y = cos 1 3 x 27. y = sin 3x 28. y = cos 2x 29. y = 2 sin 1 4 x 30. y = 3 sin 1 6 x 31. y = -2 cos 3x 32. y = -5 cos 2x 33. y = cos px 34. y = -sin px 35. y = -2 sin 2px 36. y = 3 cos 2px 37. y = 1 2 cos p 2 x 38. y = - 2 3 sin p 4 x 39. y = p sin px 40. y = -p cos px
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