Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 8 - Section 8.2 - Graphs of Polar Equations - 8.2 Exercises - Page 600: 15

Answer

1. the function is symmetric with respect to the polar axis. 2. the function is symmetric with respect to the pole. 3. the function is symmetric with respect to the line $\theta=\frac{\pi}{2}$.

Work Step by Step

1. Test the polar equation for symmetry with respect to the polar axis : replace $\theta$ with $-\theta$, we have $r^2=4cos2(-\theta)=4cos2(\theta)$ which is the same as the original, so the function is symmetric with respect to the polar axis. 2. Test the polar equation for symmetry with respect to the pole : replace $r$ with $-r$, we have $(-r)^2=r^2=4cos2(\theta)$ which is the same as the original, so the function is symmetric with respect to the pole. 3. Test the polar equation for symmetry with respect to the line $\theta=\frac{\pi}{2}$: replace $\theta$ with $\pi-\theta$, we have $r^2=4cos2(\pi-\theta)=4cos2(\theta)$ which is the same as the original, so the function is symmetric with respect to the line $\theta=\frac{\pi}{2}$.
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.