1. Objective: Polar coordinate system. Coordinate conversion.
Warm up
Prove the half angle identity for Tangent.

2. Polar coordinate system:
If r > 0, then P is on the terminal side of .
If r < 0, then P is on the terminal side of

3. Polar coordinate system:

4. Example 1
Plot the points with the given polar coordinates. A B C D E

5. Coordinate Conversion: Rectangular to Polar: Polar to rectangular: Proof:

6. Example 2 Convert from polar to rectangular coordinates. a. b
Example 2 Convert from polar to rectangular coordinates. a. b. Example 3 Convert from rectangular to polar coordinates.

7. b. c. Finding all polar coordinates of a point P. or

8. Example 4
Find another representation of point in which:
a. r is positive and
r is negative and
r is positive and

9. Assignment Pg 672 #1-10, 16,18, 20-22, 27, 34, 35, 42, 43.