641 6.4 Translations of the Graphs of the Sine and Cosine Functions 18. Concept Check Refer to Exercise 17. Which one of the two graphs, y = sin x + 1 or y = sin1x + 12, is the same as the graph of y = 1 + sin x? Concept Check Match each function in Column I with the appropriate description in Column II. I 19. y = 3 sin12x - 42 20. y = 2 sin13x - 42 21. y = -4 sin13x - 22 22. y = -2 sin14x - 32 II A. amplitude = 2, period = p 2 , phase shift = 3 4 B. amplitude = 3, period = p, phase shift = 2 C. amplitude = 4, period = 2p 3 , phase shift = 2 3 D. amplitude = 2, period = 2p 3 , phase shift = 4 3 Concept Check Fill in each blank with the word right or the word left. 23. If the graph of y = cos x is translated horizontally to the p 2 units, it will coincide with the graph of y = sin x. 24. If the graph of y = sin x is translated horizontally to the p 2 units, it will coincide with the graph of y = cos x. For each function, give the amplitude, period, vertical translation, and phase shift, as applicable. See Examples 1 – 5. 31. y = 2 sin1x + p2 32. y = 3 sin ax + p 2b 33. y = - 1 4 cos a 1 2 x + p 2b 34. y = - 1 2 sin a 1 2 x + pb 35. y = 3 cos c p 2 ax - 1 2b d 36. y = -cos c p ax - 1 3b d 37. y = 2 - sin a3x - p 5b 38. y = -1 + 1 2 cos12x - 3p2 Connecting Graphs with Equations Each function graphed is of the form y = c + cos x, y = c + sin x, y = cos1x - d2, or y = sin1x - d2, where d is the least possible positive value. Determine an equation of the graph. 25. 26. x y 0 –1 –2 –3 1 2 2p p x y 0 –1 –2 1 2 3 2p p 27. 28. x y 0 –2 –1 2 1 2p p p 3 x y 0 –2 2 1 2p 3 5p 3 p p 3 – –1 29. 30. x y 0 –2 –1 2 1 2p p x y 0 –2 –1 2 1 2p p
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