1. Copyright © 2011 Pearson, Inc. 6.4 Polar Coordinates

2. Copyright © 2011 Pearson, Inc. Slide 6.4 - 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. Copyright © 2011 Pearson, Inc. Slide 6.4 - 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. Copyright © 2011 Pearson, Inc. Slide 6.4 - 4 Example Plotting Points in the Polar Coordinate System

5. Copyright © 2011 Pearson, Inc. Slide 6.4 - 5 Example Plotting Points in the Polar Coordinate System

6. Copyright © 2011 Pearson, Inc. Slide 6.4 - 6 Finding all Polar Coordinates of a Point

7. Copyright © 2011 Pearson, Inc. Slide 6.4 - 7 Coordinate Conversion Equations

8. Copyright © 2011 Pearson, Inc. Slide 6.4 - 8 Example Converting from Polar to Rectangular Coordinates

9. Copyright © 2011 Pearson, Inc. Slide 6.4 - 9 Example Converting from Polar to Rectangular Coordinates

10. Copyright © 2011 Pearson, Inc. Slide 6.4 - 10 Example Converting from Rectangular to Polar Coordinates

11. Copyright © 2011 Pearson, Inc. Slide 6.4 - 11 Example Converting from Rectangular to Polar Coordinates

12. Copyright © 2011 Pearson, Inc. Slide 6.4 - 12 Example Converting from Polar Form to Rectangular Form

13. Copyright © 2011 Pearson, Inc. Slide 6.4 - 13 Example Converting from Polar Form to Rectangular Form

14. Copyright © 2011 Pearson, Inc. Slide 6.4 - 14 Example Converting from Polar Form to Rectangular Form

15. Copyright © 2011 Pearson, Inc. Slide 6.4 - 15 Example Converting from Polar Form to Rectangular Form

16. Copyright © 2011 Pearson, Inc. Slide 6.4 - 16 Example Converting from Polar Form to Rectangular Form

17. Copyright © 2011 Pearson, Inc. Slide 6.4 - 17 Quick Review

18. Copyright © 2011 Pearson, Inc. Slide 6.4 - 18 Quick Review Use the Law of Cosines to find the measure of the third side of the given triangle. 4. 40 º 8 10 5. 35 º 6 11

19. Copyright © 2011 Pearson, Inc. Slide 6.4 - 19 Quick Review Solutions

20. Copyright © 2011 Pearson, Inc. Slide 6.4 - 20 Quick Review Solutions Use the Law of Cosines to find the measure of the third side of the given triangle. 4. 40 º 8 10 5. 35 º 6 11 6.4 7