1. Give 4 different pairs of polar coordinates that correspond to the Cartesian Coordinates (2,2)

2. 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.

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

4. r=10 r= ̶ 10 Negative radius means go in the opposite directions
Remember to consider the rotation FIRST
r=10
r= ̶ 10

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

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

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

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

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

10. Example
Graph: θ=
What about

11. Some Classic Polar Graphs
Example
Some Classic Polar Graphs
limacon

12. Example
A Classic Polar Graph
Spiral of Archimedes

13. Some Classic Polar Graphs
Example
Some Classic Polar Graphs
8 petal rose

14. Use your graphing calculator to graph
CARDIOID
MODE
POL Y=
GRAPH

15. Important Idea 8
4 petals
Polar Roses

16. Important Idea 10
8 petals
Polar Roses

17. Try This
Name the angle in rads?
Polar Roses

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

19. Some Calculus
Find the slope of at
Demana text ex 5 p.552

20. We can write polar equations parametrically
where