1. Let 1/J(t) = (asint,acost), O"(t) = (acos2t,asin2t), 1= [0, 27r), and J = [0,7r).

Sketch the traces of (1/J, I) and (0", J). Note the "direction of flight" and the

"speed" of each parametrization. Compare these parametrizations with the one given in Example 13.4.