MATH10560 Midterm: Math10560Solutions ExtraQuestions Ex3
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1. (6 pts) which of the following is a graph of the parametric curve de ned by x = 2t cos (t) y = t sin (t) for 0 t 2 ? y. Observe that when t = 0 we get that x = 2(0) cos(0) = 0 and y = 0 sin(0) : thus the point (0, 0) is on the curve. When t = pi we see that x = 2 cos( ) = 2 and y = sin( ) = 0. Thus the point ( 2 , 0) is on the curve. The graph in (a) is the only one where the curve passes through these both these points. (a) We check the values of x and y at some speci c values of t: at t = 0, (x, y) = (0, 1). Joining the dots, we see that the answer has to be iii. (b)
