Precalculus (6th Edition) Blitzer

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

Chapter 6 - Section 6.3 - Polar Coordinates - Exercise Set - Page 742: 36


The rectangular coordinates of $\left( 2,\frac{\pi }{6} \right)$ are $\left( \sqrt{3},1 \right)$.

Work Step by Step

The rectangular coordinates of the point are $\left( x,y \right)$. Now, rewrite the rectangular coordinates in terms of polar coordinates, $x=r\cos \theta \ \text{ and }\ y=r\sin \theta $ …… (I) Substituting the values of $r\ \text{ and }\ \theta $ in (I) we get, $\begin{align} & x=2\cos \frac{\pi }{6} \\ & =2\times \frac{\sqrt{3}}{2} \\ & =\sqrt{3} \end{align}$ And $\begin{align} & y=2\sin \frac{\pi }{6} \\ & =2\times \frac{1}{2} \\ & =1 \end{align}$ Therefore, the rectangular coordinates of $\left( 2,\frac{\pi }{6} \right)$ are $\left( \sqrt{3},1 \right)$.
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.