Work Step by Step
If a polar equation passes a symmetry test, then that symmetry is exhibited by its graph. By contrast, if a polar equation fails a symmetry test, then its graph may or may not have that kind of symmetry. Therefore, the graph of a polar equation may have a symmetry even if it fails a test for that particular symmetry. Nevertheless, the symmetry tests are useful. If we detect symmetry, we can obtain a graph of the equation by plotting fewer points.