1. Section 12.5 - The Polar Coordinate System 12.1

2. The keys……

6. Four Translations Point - Polar to Rectangular Point - Rectangular to Polar Equation - Polar to Rectangular Equation - Rectangular to Polar

7. Point – Polar to Rectangular

8. Point – Rectangular to Polar

9. Equation - Polar to Rectangular

10. Equation - Rectangular to Polar

11. Shapes of Polar Curves Graphing Polar Curves on Calculator Finding Points of Intersection (Boundaries of Integration)

12. The Shapes Lines Circles Cardioid Lemniscate Sprial Rose Curves

13. The Shapes - Lines Vertical Line Horizontal Line General Line

14. The Shapes - Circles

15. The Shapes – Cardioids (Hearts) Note: Extra loop Only if b > a

16. The Shapes – Lemniscates (Propellers)

17. The Shapes - Spirals

18. The Shapes – Rose Curves n even – 2n pedals n odd – n pedals

19. Graphing Polar Curves on Calculator 1. Change mode to Polar 2. Hit y = (you’ll see r = indicating polar mode) 3. Enter the equation 4.Graphing once should give you a sense of how to change the x, y and theta constraints.

20. 5. Now change the constraints in WINDOW

21. Finding Points of Intersection (Boundaries of Integration)

22. WRONG ANSWER