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: 55


To test for symmetry with respect to the pole (origin), replace r with –r; if an equivalent equation results, the graph is symmetric with respect to the pole.

Work Step by Step

For example: We will replace $r\,\text{with}\,-r$ in the polar equation $r=1-2\cos \theta $, to perform the test for the pole, $\begin{align} & r=1-2\cos \theta \\ & -r=1-2\cos \theta \end{align}$ The resultant equation changes and thus it fails this symmetry test.
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