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: 7


The graph is symmetric only with respect to the line $\theta =\frac{\pi }{2}$.

Work Step by Step

We make the substitutions as follows: (a) $\theta \to - \theta$ :$$r= \sin (- \theta ) \quad \Rightarrow \quad r=-\sin \theta$$ (b) $r \to -r, \quad \theta \to -\theta$ :$$-r = \sin (-\theta ) \quad \Rightarrow \quad r= \sin \theta$$ (c) $r \to -r$ :$$-r = \sin \theta \quad \Rightarrow \quad r=-\sin \theta$$
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