1. 6.4
Polar Coordinates

2. What you’ll learn about
Polar Coordinate System
Coordinate Conversion
Equation Conversion
Finding Distance Using Polar Coordinates
… and why
Use of polar coordinates sometimes simplifies
complicated rectangular equations and they are useful in
calculus.

3. The Polar Coordinate System
A polar coordinate system is a plane with a point O, the pole, and a ray from O, the polar axis, as shown. Each point P in the plane is assigned polar coordinates as follows: r is the directed distance from O to P, and  is the directed angle whose initial side is on the polar axis and whose terminal side is on the line OP.

4. Example Plotting Points in the Polar Coordinate System

5. Example Plotting Points in the Polar Coordinate System

6. Finding all Polar Coordinates of a Point

7. Coordinate Conversion Equations

8. Example Converting from Polar to Rectangular Coordinates

9. Example Converting from Polar to Rectangular Coordinates

10. Example Converting from Rectangular to Polar Coordinates

11. Example Converting from Rectangular to Polar Coordinates

12. Example Converting from Polar Form to Rectangular Form

13. Example Converting from Polar Form to Rectangular Form

14. Example Converting from Polar Form to Rectangular Form

15. Example Converting from Polar Form to Rectangular Form

16. Example Converting from Polar Form to Rectangular Form

17. Quick Review

18. Quick Review
Use the Law of Cosines to find the measure of the third side of the given triangle. 4.
40º 8 10 5.
35º 6 11

19. Quick Review Solutions

20. Quick Review Solutions
Use the Law of Cosines to find the measure of the third side of the given triangle. 4.
40º 8 10 5.
35º 6 11
6.4 7