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: 34

Answer

The graph is symmetric with respect to the line $\theta =\frac{\pi }{2}$.
1585030579

Work Step by Step

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

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.