Chapter 9.2, Problem 9AYU

To determine

To fill: What has to be replaced to test whether the graph of a polar equation may be symmetric with respect to the polar axis instead $\theta$.

Answer to Problem 9AYU

Solution:

To test whether the graph of a polar equation may be symmetric with respect to the polar axis instead of $\theta$ by $- \theta$.

Given:

Statement asked the replacement term to test whether the graph of a polar equation may be symmetric with respect to the polar axis instead of $\theta$.

Explanation of Solution

Test for symmetry:

Symmetry with respect to the polar axis ($x$-Axis):

In a polar equation, replace $\theta$ by $- \theta$. If an equivalent equation results, the graph is symmetric with respect to the polar axis.