A point P on the rim of a wheel of radius a is initially at the origin. As the wheel rolls to the right along the x-axis, P traces out a curve called a cycloid (see Figure 18). Derive parametric equations for the cycloid as follows. The parameter is θ.
(a) Show that OT = aθ
(b) Convince yourself that PQ = a sin θ, QC = a cos θ, 0 ‰¤ 0 ‰¤ Ï€/2.
(c) Show that x = a(θ - sin θ), y = a(1 - cos θ).

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Cycloid Pa, y) 0