1. Graphs of Polar Coordinates Sections 6.4

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

3. 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)

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 a a ≠ 0

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