1. 6.5 Graphs of Polar Equations

2. I. General Form
A.) Graphs of Polar Functions- An infinite collection of rectangular coordinates (x, y) can be represented by an equation in terms of x and/or y.
Collections of polar coordinates can be represented in a similar fashion, where

3. On your TI-83+, change your MODE to POLAR
On your TI-83+, change your MODE to POLAR. Set your window to [0,2π];[-5,5]; [-5,5] and graph
This direction
Start (0,0)

4. B.) Ex. 1- Try a few of these.
Make a table!!!

8. II. Analyzing Polar Equations
A.) Characteristics of a Polar:
(Much the same as the characteristics of a rectangular equation.)

9. B.) Symmetry Tests -
TEST REPLACE WITH
x-axis
y-axis
Origin

10. NO! YES! NO! C.) Ex. 2- Determine the symmetry for x-axis: y-axis:
Origin:
NO!
YES!
NO!

11. D.) Ex. 3 - Analyze

12. E.) Ex. 4 – Use the graph from example 1 to analyze

13. F.) Ex. 5 – Use your graphing calculator to analyze the following polar equations:

15. III. Rose Curves
A.) Def. – A ROSE CURVE is any polar equation in the form of where n is an integer greater than 1.
If n is odd, there are n petals.
If n is even, there are 2n petals.

16. B.) For all rose curves .

17. MORE EXCITEMENT TO COME TOMORROW!!!!!

18. IV. Limaçon Curves A.) Any polar equation in the form of is called
a LIMAÇON (“leemasahn” or “snail”) CURVE.

19. B.) Ex. 6- Analyze

20. C.) In general-

21. V. Lemniscate Curves
A.) Any polar equation in the form of or is called a LEMNISCATE CURVE.

22. B.) Ex. 7- Analyze

23. C.) In general-

24. VI. The Spiral of Archimedes
A.) The polar equation is called THE SPIRAL OF ARCHIMEDES.

25. B.) Ex. 8- Analyze