symmetry with respect to the polar axis replace with (check for equivalent equation)
symmetry with respect to the line replace with and r with r (check for equivalent equation)
symmetry with respect to the pole replace r with r (check for equivalent equation)
4 Symmetry Tests
If a polar equation passes a symmetry test then its graph exhibits that symmetry
If a polar equation does not pass a symmetry test then its graph may or may not exhibit that symmetry.
5 Test for symmetry and then graph the polar equation 6 Circles in Polar Coordinates a a 7 Test for symmetry and then graph the polar equation 8 Limaçons in Polar Coordinates 9 Test for symmetry and then graph the polar equation 10 Lemniscates in Polar Coordinates a 0 a a 11 Rose Curves in Polar Coordinates If n is even the rose has 2n petals. If n is odd the rose has n petals. a is the distance from the tip of the petal to the pole
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