Graphs of Polar Coordinates

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 —θand 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