Precalculus (6th Edition) Blitzer

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

Chapter 6 - Mid-Chapter Check Point - Page 756: 30

Answer

Only symmetric with respect to the polar axis; see graph.

Work Step by Step

Step 1. We are given the polar equation $r=2-4cos\theta$. To test the symmetry with respect to the polar axis, let $\theta\to -\theta$; we have $r=2-4cos(-\theta)$ or $r=2-4cos\theta$. Thus, the equation is symmetric with respect to the polar axis. Step 2. To test the symmetry with respect to the line $\theta=\frac{\pi}{2}$, let $r\to -r$ and $\theta\to -\theta$; we have $-r=2-4cos(-\theta)$ or $r=-2+4cos\theta$; thus the equation is not symmetric with respect to the line $\theta=\frac{\pi}{2}$. Step 3. To test the symmetry with respect to the pole, let $r\to -r$; we have $-r=2-4cos\theta$ or $r=-2+4cos\theta$. Thus, the equation is not symmetric with respect to the pole. Step 4. We can graph the equation 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.