Symmetry In Polar Curves

Symmetry in Polar Curves

Graphing polar curves can be difficult, so it is good to recognize certain properties of polar curves and symmetry which can help us graph them.

Property 1: For a polar equation in the form $r = f(\theta)$, if $f(\theta) = f(-\theta)$, then the curve is symmetric about the polar axis
Property 2: For a polar equation in the form $r = f(\theta)$, if $f(\theta) = f(\theta + \pi)$, then the curve is symmetric about the pole. Alternatively, if $r = -r$, then the same property holds.
Property 3: For a polar equation in the form $r = f(\theta)$, if $f(\theta) = f(\pi - \theta)$, then the curve is symmetric about the polar equation $\theta = \frac{\pi}{2}$.
Unless otherwise stated, the content of this page is licensed under Creative Commons Attribution-ShareAlike 3.0 License