Symmetry In Polar Curves
 Table of Contents

# 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 $\theta = \frac{\pi}{2}$.
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