## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 6 - Section 6.7 - The Dot Product - Exercise Set - Page 799: 55

#### Answer

Equation may only be symmetric with respect to the polar axis. See graph. #### Work Step by Step

Step 1. To test the symmetry with respect to the polar axis, replace $(r,\theta)$ with $(r,-\theta)$; we have $r =1-2cos(-\theta)$ or $r =1-2cos(\theta)$ . Thus the equation is symmetric with respect to the polar axis. Step 2. To test the symmetry with respect to the line $\theta=\frac{\pi}{2}$, replace $(r,\theta)$ with $(-r,-\theta)$; we have $-r =1-2cos(-\theta)$ or $r =-1+2cos(\theta)$ . Thus the equation may not be symmetric with respect to the line $\theta=\frac{\pi}{2}$. Step 3. To test the symmetry with respect to the pole, replace $(r,\theta)$ with $(-r,\theta)$; we have $-r =1-2cos(\theta)$ or $r =-1+2cos(\theta)$ . Thus the equation may not be symmetric with respect to the pole. Step 4. Using test points with $0\leq\theta\leq2\pi$, we can graph the equation as shown in the figure.

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