Precalculus (6th Edition) Blitzer

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

Chapter 6 - Section 6.7 - The Dot Product - Exercise Set - Page 799: 50

Answer

Only symmetric with respect to the polar axis. See graph.
1584144615

Work Step by Step

Step 1. To test the symmetry with respect to the polar axis, replace $(r,\theta)$ with $(r,-\theta)$; we have $r =3cos(-\theta)$ or $r =3cos(\theta)$. Thus the equation is symmetric with respect to the polar axis. Step 2. To test the symmetry with respect to the line $\theta=\frac{\pi}{2}$, replace $(r,\theta)$ with $(-r,-\theta)$; we have $-r =3cos(-\theta)$ or $r =-3cos(\theta)$. Thus the equation is not necessarily symmetric with respect to the line $\theta=\frac{\pi}{2}$. Step 3. To test the symmetry with respect to the pole, replace $(r,\theta)$ with $(-r,\theta)$; we have $-r =3cos(\theta)$ or $r =-3cos(\theta)$. Thus the equation is not necessarily symmetric with respect to the pole. Step 4. Use test points with $0\leq\theta\leq\pi$, we can graph the function as shown in the figure.
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.