Let (t) = (a sin t, a cos t, (t) = (a cos 2t, a sin 2t,

Let ψ(t) = (a sin t, a cos t, σ(t) = (a cos 2t, a sin 2t, I = [0, 2π), and J = [0, π). Sketch the traces of (ψ, I) and (σ, J). Note the "direction of flight" and the "speed" of each parametrization. Compare these parametrizations with the one given in Example 13.4.