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 - Concept and Vocabulary Check - Page 753: 4


To test whether the graph of a polar equation may be symmetric with respect to the line $\theta =\frac{\pi }{2}$ $\left( \text{y-axis} \right)$, replace $\left( r,\theta \right)$ with $\left( -r,-\theta \right)$.

Work Step by Step

When $\left( r,\theta \right)$ is replaced with $\left( -r,-\theta \right)$, if the resultant polar equation is equivalent to given polar equation then a graph of a polar equation exhibits symmetry with respect to the line $\theta =\frac{\pi }{2}$ $\left( \text{y-axis} \right)$.
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