## Precalculus (6th Edition) Blitzer

(a) From the graph it can be seen that \begin{align} & \sin t=\frac{PB}{a} \\ & =\frac{XA}{a} \end{align} $XA=a\sin t$ And the length OA is equal to the length of arc PA The length of arc PA is $at$. Now, \begin{align} & x=OA-xA \\ & =at-a\sin t \\ & =a\left( t-\sin t \right) \end{align} Thus, the parametric equation for x is $x=a\left( t-\sin t \right)$. (b) \begin{align} & \cos t=\frac{BC}{a} \\ & BC=a\cos t \end{align} Also, $AC=a$ Then, \begin{align} & y=AC-BC \\ & =a-a\cos t \\ & =a\left( 1-\cos t \right) \end{align} Thus, the parametric equation for y is given by $y=a\left( 1-\cos t \right)$.