1. Definition
A Polar Coordinate System is a method of locating a point (r, ) in a plane where r is a distance from a point called the pole directed at an angle θ measured counterclockwise from a polar axis.

2. Example
r=10
Pole
Polar Axis
Polar Grid
(r,θ )=

3. r=10 r= ̶ 10 Negative radius means go in the opposite directions
Consider the rotation FIRST
r=10
r= ̶ 10

4. Example
Find the polar coordinates:
(r,θ )=

5. Example
Find the polar coordinates:
(r,θ )=

6. Plot
Name the point with three other polar coordinates using

7. Important Idea
Polar coordinates are related to rectangular coordinates as follows: r y θ x

8. Example
Graph:
r=6
What about
r = ̶ 6?

9. Example
Graph: θ=
What about

10. Try This
Write the polar equation of the circle with center (4,0) and radius 4.
(Hint: Start with the rectangular equation)

15. Roses 8
4 petals
Polar Roses

16. Important Idea 10
8 petals
Polar Roses

17. Important Idea
What do you observe about the number of petals? The period?