Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 9 - Section 9.5 - Parametric Equations - Exercise Set - Page 1021: 92


See the full explanation below:

Work Step by Step

(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 $y=a\left( 1-\cos t \right)$.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.