1. PPT Review

2. Polar Coordinates and Graphing
r = directed distance
= directed angle
Polar Axis O
Counterclockwise from polar axis to .

3. Plotting Points in the Polar Coordinate System
The point lies two units from the pole on the terminal side of the angle
The point lies three units from the pole on the terminal side of
the angle
The point coincides with
the point

4. Multiple Representations of Points

5. Example of Multiple Representations from -360°≤ x ≤360°
1.) (100 , 50°)
2.) (1.2 , 70°)
(100 , -310°)
(-100 , 230°)
(-100 , -130°)
(1.2 , -290°)
(-1.2 , 250°)
(-1.2 , -110°)

6. Try plotting the following points in polar coordinates and find
three additional polar representations of the point:
Make sure to go over “sliding” through the pole to opposite ray when negative r is used.

8. Summary of Special Polar Graphs
Limacons:
Limacon with
inner loop
Cardiod
(heart-shaped)
Dimpled
Limacon
Convex
Limacon

9. Rose Curves:

10. Circles and Lemniscates
Note that a is the length of the diameter of the circles and length of the loop of a lemnicscate.

11. MATCH THE POLAR GRAPH WITH IT’S EQUATION
5. 6. 2 4 3 5 6 1

12. MATCH THE POLAR GRAPH WITH IT’S EQUATION 2 4 3 1

13. Graphing a Polar Equation
circle
Note that some points are “retraced” as you mark them.

14. Using Symmetry to Sketch
Limacon DImpled
Remind students of even/odd properties:
cos(-u)=cos u
sin(-u)=-sin u

15. You can see that the graph is symmetric with respect to the line
Spiral of Archimedes

16. Graph This:
Rose Curve with 2b petals = 4 petals

17. Graph each of these:
Convex Limacon
Cardioid Limacon

18. This type of graph is called a cardioid.
Scale of this graph is 0.25

19. This type of graph is called a limacon without an inner loop.
Let's let each unit be 1.
Let's plot the symmetric points

20. This type of graph is called a limacon with an inner loop.
Let's let each unit be 1/2.
Let's plot the symmetric points

21. This type of graph is called a rose with 4 petals.
Let's let each unit be 1/2.
Let's plot the symmetric points

22. This type of graph is called a lemniscate
Let's let each unit be 1/4.