## Trigonometry (11th Edition) Clone

Published by Pearson

# Chapter 8 - Complex Numbers, Polar Equations, and Parametric Equations - Section 8.5 Polar Equations and Graphs - 8.5 Exercises - Page 396: 74g

#### Answer

In general, the completed statements in parts (a)-(e) mean that the graphs of polar equations of the form $r = a \pm b~sin~\theta$ (where $a$ may be 0) are symmetric with respect to the vertical line $\theta = \frac{\pi}{2}$

#### Work Step by Step

Note that $~~sin~(\pi-\theta) = sin~\theta$ According to part (b), the graph of $r = f(\theta)$ is symmetric with respect to the vertical line $\theta = \frac{\pi}{2}$ if substitution of $\pi-\theta$ for $\theta$ leads to an equivalent equation. In general, the completed statements in parts (a)-(e) mean that the graphs of polar equations of the form $r = a \pm b~sin~\theta$ (where $a$ may be 0) are symmetric with respect to the vertical line $\theta = \frac{\pi}{2}$

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