to test for symmetry in polar equations for $$\large \begin{array}{llll} symmetry\ to&replace \\\hline\\ x-axis\textit{ or polar axis}&\theta\to -\theta \\ \quad \\ y-axis\textit{ or the }\frac{\pi}{2}\ linej&\theta\to \pi-\theta \\ \quad \\ origin\textit{ or the pole}&\theta\to \pi+\theta \end{array}$$ once you replace those values, to the original polar equation and if you get the "same original" back when simplifying, then it has symmetry in relation to that axis if not, then, well, it doesn't :)