Question: Graph the following more complicated curves: (a) r(t) = [2 cos t + cos 2t, 2 sin t - sin 2t] (Steiners hypocycloid). (b) r
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).
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