6.5 Graphs of Polar Equations

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

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)

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

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

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

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

D.) Ex. 3 - Analyze

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

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

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.

B.) For all rose curves .

MORE EXCITEMENT TO COME TOMORROW!!!!!

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

B.) Ex. 6- Analyze

C.) In general-

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

B.) Ex. 7- Analyze

C.) In general-

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

B.) Ex. 8- Analyze