Example 11: The cycloid

As a circle rolls along the $x$ -axis, a point on its perimeter traces a curve known as a cycloid. These are the parametric equations for a cycloid:

$$\left. \begin{array}{lclcl} x &=& f(t) &=& t-\sin t\\ y &=& g(t) &=& 1-\cos t\\ \end{array}\right\}\quad 0\leq t\leq10\pi$$