Precalculus (6th Edition) Blitzer

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

Chapter 6 - Section 6.4 - Graphs of Polar Equations - Exercise Set - Page 754: 53


To test the symmetry with respect to the polar axis, replace $\theta \,\text{with}\,-\theta $. If an equivalent equation results, then the graph is symmetric with respect to the polar axis.

Work Step by Step

For example: We will replace $\theta \,\text{with}\,-\theta $ in the polar equation $r=1-2\cos \theta $ to perform the test for the polar axis, $\begin{align} & r=1-2\cos \left( -\theta \right) \\ & r=1-2\cos \theta \\ \end{align}$ The resultant equation remains the same. Thus, the equation is symmetric with respect to the polar axis.
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.