1. The Polar Coordinate System
The Polar Coordinate System is a coordinate plane based on the dimensions r and q.

2. Points on a Polar Graph
A point on a polar coordinate plane is given by the ordered pair, (r, q), where:
r = distance from origin to point
q = angle in standard position to the point

3. The Polar Grid

4. Plotting a Point

5. More Than One Ordered Pair Can Describe a Point

6. Negative ‘r’ Values

7. Name 4 Ordered Pairs

8. #1: Counter-Clockwise

9. #2: Clockwise (negative q)

10. #3: CCW/flipped (neg. r)

11. #3: CW/flipped (neg. q & neg. r)

12. Name 4 Ordered Pairs

13. Try these Plot (3, 120°) Plot (- 5, 210°) Plot (4 , - 90°)

14. Try these Name three other ordered pairs for the point (5,- 100°).

15. Basic Polar Graphs
We graph Equations in the Polar Coordinate System that are in terms of r and q.
We will consider the following:
r = k (r = a constant)
q = k (q = a constant)

16. Graph r = k
The coordinate, r, tells us how far from the origin to put a point. The equation r = 4 stands for :
‘all the points that are 4 units from the origin’.
What would the graph of all these points look like?

17. r = 4 is a CIRCLE

18. Graph q = k The coordinate, q, tells us along what angle a point lies.
The equation q = 120° stands for :
‘all the points that are along the 120° line’.
What would the graph of all these points look like?

19. q = 120° is a LINE
Notice the line is in both quadrants 2 & 4. The points in quadrant 4 are points with q = 120° and a NEGATIVE value for r.

20. Summary
Points in a Polar Grid are given by (r, q) - the values of r and q can be positive or negative.
Each point can be given by several different ordered pairs.
The polar equation r = k is a circle.
The polar equation q = k is a line.