# Chapter 6 - Section 6.4 - Graphs of Polar Equations - Exercise Set - Page 754: 20

The graph does not necessarily have symmetry with respect to the polar axis, the line $\theta =\frac{\pi }{2}$, or the pole. See the graph below:

#### Work Step by Step

We look for symmetry by making the following substitutions: (a) $\theta \to - \theta$ :$$r=2-\sin (- \theta ) \quad \Rightarrow \quad r=2+\sin \theta$$Thus, the graph does not necessarily have symmetry with respect to the polar axis. (b) $r \to -r, \quad \theta \to -\theta$ :$$-r =2-\sin (-\theta ) \quad \Rightarrow \quad r=-2-\sin \theta$$Thus, the graph does not necessarily have symmetry with respect to the line $\theta=\frac{\pi}{2}$. (c) $r \to -r$ :$$-r =2-\sin \theta \quad \Rightarrow \quad r=-2+\sin \theta$$Thus, the graph does not necessarily have symmetry with respect to the pole.

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