Section 6.4 Graphs of Polar Equations

1. Section 6.4Graphs of Polar Equations MA.PC.6.3 2000 Graph equations in the polar coordinate plane.

2. Graphing a Polar Equation by Point Plotting • A polar equation is an equation whose variables are and . The graph of a polar equation is the set of all points whose polar coordinates satisfy the equation. We use polar grids to graph polar equations.

3. This type of graph is called a ROSE WITH 4 PETALS. Let's let each unit be 1/2.

4. Classical Curves • Circle • Rose • Lemniscate • Limacon • Cardioid

5. CIRCLES Equations of circles would look like one of the following:

6. ROSE Equations of rose curves would look like one of the following: Where even has petals and odd has petals.

7. LEMNISCATE Equations of lemniscates would like one of the following:These graphs will pass through the pole and are propeller shaped. Unit is 1/4

8. LIMAÇON Equations of limaçons would like one of the following:If there is an inner loop.If there is an indentation. Unit is 1/2

9. CARDIOD Equations of cardiods would like one of the following:All graphs of cardiods pass through the pole. Unit is 1/4

10. Example • Graph the equation

11. Example • Graph the equation

12. Example • Graph the equation

13. Example • Graph the equation

15. Homework • Worksheet