(a) Use a graphing utility to graph each set of parametric equations.

(b) Compare the graphs of the two sets of parametric equations in part (a). When the curve represents the motion of a particle and is time, what can you infer about the average speeds of the particle on the paths represented by the two sets of parametric equations?
(c) Without graphing the curve, determine the time required for a particle to traverse the same path as in parts (a) and (b) when the path is modeled by

x = t - sint, y = 1- cos t, 0 t 2 x = 2t sin(2t), y = 1- cos(2t), - 0 t