Graphs of Polar Coordinates Sections 6.4

Objectives Use point plotting to graph polar equations. Use symmetry to graph polar equations.

Symmetry Tests symmetry with respect to the polar axis — replace θ with —θ (check for equivalent equation) symmetry with respect to the line — replace θ with —θ and r with —r (check for equivalent equation) symmetry with respect to the pole — replace r with —r (check for equivalent equation)

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.

Test for symmetry and then graph the polar equation

Circles in Polar Coordinates a a

Test for symmetry and then graph the polar equation

Limaçons in Polar Coordinates

Test for symmetry and then graph the polar equation

Lemniscates in Polar Coordinates a a a ≠ 0

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