Precalculus (6th Edition) Blitzer

To test the symmetry with respect to the polar axis, replace $\theta \,\text{with}\,-\theta$. If an equivalent equation results, then the graph is symmetric with respect to the polar axis.
For example: We will replace $\theta \,\text{with}\,-\theta$ in the polar equation $r=1-2\cos \theta$ to perform the test for the polar axis, \begin{align} & r=1-2\cos \left( -\theta \right) \\ & r=1-2\cos \theta \\ \end{align} The resultant equation remains the same. Thus, the equation is symmetric with respect to the polar axis.