Graph the following more complicated curves:

(a) r(t) = [2 cos t + cos 2t, 2 sin t - sin 2t] (Steiner’s hypocycloid).

(b) r (t) = [cos t + k cos 2t, sin t - k sin 2t] with k = 10, 2, 1, 1/2, 0, -1/2, -1.

(c) r(t) = [cos t,    sin 5t] (a Lissajous curve).

(d) r(t) = [cos t,    sin kt]. For what k’s will it be closed?

(e) r(t) = [R sin ωt + ωRt, R cos ωt + R] (cycloid).