858 CHAPTER 8 Applications of Trigonometry 23. x = 2 + sin t, y = 1 + cos t, for t in 30, 2p4 24. x = 1 + 2 sin t, y = 2 + 3 cos t, for t in 30, 2p4 25. x = t + 2, y = 1 t + 2 , for t ≠-2 26. x = t - 3, y = 2 t - 3 , for t ≠3 27. x = t + 2, y = t - 4, for t in 1-∞, ∞2 28. x = t2 + 2, y = t2 - 4, for t in 1-∞, ∞2 Graph each plane curve defined by the parametric equations for t in 30, 2p4. Then find a rectangular equation for the plane curve. See Example 3. 29. x = 3 cos t, y = 3 sin t 30. x = 2 cos t, y = 2 sin t 31. x = 3 sin t, y = 2 cos t 32. x = 4 sin t, y = 3 cos t 33. x = 2 + sin t, y = 1 + cos t 34. x = 1 + cos t, y = sin t - 1 Give two parametric representations for the equation of each parabola. See Example 4. 35. y = 1x + 322 - 1 36. y = 1x + 422 + 2 37. y = x2 - 2x + 3 38. y = x2 - 4x + 6 39. y = x2 - 2x + 1 40. y = x2 + 4x + 4 Graph each cycloid defined by the given equations for t in the interval 30, 4p4. See Example 5. 41. x = 2t - 2 sin t, y = 2 - 2 cos t 42. x = t - sin t, y = 1 - cos t 43. x = 0.51t - sin t2, y = 0.511 - cos t2 44. x = 0.251t - sin t2, y = 0.2511- cos t2 Lissajous Figures The screen shown here is an example of a Lissajous figure. Such figures occur in electronics and may be used to find the frequency of an unknown voltage. Graph each Lissajous figure for t in 30, 6.54 using the window 3-6, 64 by 3-4, 44. 45. x = 3 sin 4t, y = 3 cos 3t 46. x = 4 sin 4t, y = 3 sin 5t −4 −6 4 6 (Modeling) Do the following. See Examples 6 – 8. (a) Determine parametric equations that model the path of the projectile. (b) Determine a rectangular equation that models the path of the projectile. (c) Determine the total flight time, to the nearest tenth of a second, and the horizontal distance traveled, to the nearest foot. 47. Flight of a Model Rocket A model rocket is launched from the ground with velocity 48 ft per sec at an angle of 60° with respect to the ground. 48. Flight of a Golf Ball Tyler is playing golf. He hits a golf ball from the ground at an angle of 60° with respect to the ground at velocity 150 ft per sec. 608
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