1. JMerrill, 2010

2.  Coordinate Conversion  To convert from polar to rectangular:  x = r cos θ  y = r sin θ  To convert from rectangular to polar:  tan θ =  x 2 + y 2 = r 2

3. 3 Multiple Representations of Points There are many ways to represent the point 123 0 When converting from one coordinate system to the other, we will only use 1 point instead of multiple representations.

4. There are 3 tests for symmetry, but they don’t always work, so we’ll use the Quick Test

5.  For equations like r = f(sin θ) Graph is symmetric to the line  For equations like r = g(cos θ ) Graph is symmetric to the polar (x) axis  See Ex. 2 on page 786—a good use of sketching using symmetry.

6. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 6 Example: Zeros and Maximum r- values Example: Find the zeros and the maximum value of r for the graph of r = 2cos . 123 0 The maximum value of r is 2. It occurs when  = 0 and 2 . These are the zeros of r. Symmetric about the polar axis