Explain why or why not Determine whether the

Chapter 10, Problem 65

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Explain why or why not Determine whether the following statements are true and give an explanation or counterexample. a. The equations x = -cos t, y = -sin t, for 0 t 2p, generate a circle in the clockwise direction. b. An object following the parametric curve x = 2 cos 2pt, y = 2 sin 2pt circles the origin once every 1 time unit. c. The parametric equations x = t, y = t2, for t 0, describe the complete parabola y = x2. d. The parametric equations x = cos t, y = sin t, for -p>2 t p>2, describe a semicircle. e. There are two points on the curve x = -4 cos t, y = sin t, for 0 t 2p, at which there is a vertical tangent line. 6