1. Sullivan Algebra and Trigonometry: Section 9.2 Polar Equations and Graphs Objectives of this Section Graph and Identify Polar Equations by Converting to Rectangular Coordinates Test Polar Equations for Symmetry Graph Polar Equations by Plotting Points

2. An equation whose variables are polar coordinates is called a polar equation. The graph of a polar equation consists of all points whose polar coordinates satisfy the equation.

3. Identify and graph the equation: r = 2 Circle with center at the pole and radius 2.

6. Let a be a nonzero real number, the graph of the equation is a horizontal line a units above the pole if a > 0 and units below the pole if a < 0.

7. Let a be a nonzero real number, the graph of the equation is a vertical line a units to the right of the pole if a > 0 and units to the left of the pole if a < 0.

10. Let a be a positive real number. Then, Circle: radius a; center at (0, a) in rectangular coordinates. Circle: radius a; center at (0, -a) in rectangular coordinates.

11. Let a be a positive real number. Then, Circle: radius a; center at (a, 0) in rectangular coordinates. Circle: radius a; center at (-a, 0) in rectangular coordinates.

12. Symmetry with Respect to the Polar Axis (x-axis):

13. Symmetry with Respect to the Line (y-axis)

14. Symmetry with Respect to the Pole (Origin):

15. Tests for Symmetry Symmetry with Respect to the Polar Axis (x-axis):

16. Symmetry with Respect to the Line (y-axis): Tests for Symmetry

17. Symmetry with Respect to the Pole (Origin):

18. Specific Types of Polar Graphs Cardioids (heart shaped) where a > 0. The graph passes through the pole. Limacons without an inner loop (French word for snail) where a > 0, b > 0, and a > b. The graph does not pass through the pole.

19. Limacons with an inner loop (French word for snail) where a > 0, b > 0, and a < b. The graph passes through the pole twice. Rose Curves If n is even and not zero, the graph has 2n petals. If n is odd and not one or negative one, the graph has n petals.

20. Lemniscates (Greek word for propeller) where a is non-zero. The graph will be propeller shaped.