870 CHAPTER 8 Applications of Trigonometry For each equation, write an equivalent equation in rectangular coordinates. 89. r = 3 1 + cos u 90. r = sin u + cos u 91. r = 2 For each equation, write an equivalent equation in polar coordinates. 92. y = x 93. y = x2 94. x2 + y2 = 25 99. Graph the plane curve defined by the parametric equations x = t + cos t, y = sin t, for t in 30, 2p4. 100. Show that the distance between 1r1, u12 and 1r2, u22 in polar coordinates is given by d = 2r1 2 + r 2 2 - 2r 1r 2 cos1u1 - u22. Find a rectangular equation for each plane curve with the given parametric equations. 101. x = 2t - 1, y = 2t , for t in 31, ∞2 102. x = 3t + 2, y = t - 1, for t in 3-5, 54 103. x = 5 tan t, y = 3 sec t, for t in a- p 2 , p 2b 104. x = t2 + 5, y = 1 t2 + 1 , for t in 1-∞, ∞ 105. x = cos 2t, y = sin t, for t in 1-p, p2 106. Give a pair of parametric equations whose graph is the circle having center 13, 42 and passing through the origin. 107. (Modeling) Flight of a Baseball A batter hits a baseball when it is 3.2 ft above the ground. It leaves the bat with velocity 118 ft per sec at an angle of 27° with respect to the ground. (a) Determine parametric equations that model the path of the baseball. (b) Determine a rectangular equation that models the path of the baseball. (c) Determine the total flight time, to the nearest tenth of a second, and the horizontal distance traveled, to the nearest foot. 108. Mandelbrot Set Consider the complex number z = 1 + i. Compute the value of z2 + z, and show that its absolute value exceeds 2, indicating that 1 + i is not in the Mandelbrot set. Find a polar equation having the given graph. 97. 95. x y 0 2 2 x = 2 96. x y 0 2 2 y = 2 x y 0 2 4 x + 2y = 4 98. x y 0 2 2 x2 + y2 = 4
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