1. Section 12.5 - The Polar Coordinate System

5. This is polar. What about rectangular? r = 2 x y

6. The keys…… PointEquation Rectangular(x, y)y = Polar

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

8. Point – Polar to Rectangular

9. Point – Rectangular to Polar

10. Equation - Polar to Rectangular

11. Equation - Rectangular to Polar

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

13. The Shapes Lines Circles Cardioid Lemniscate Sprial Rose Curves

14. Lines in rectangular:

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

16. Circles in rectangular: Centered at the origin: On one of the axis Passing through the origin The general form gets too complicated in other situations.

17. The Shapes - Circles

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

19. The Shapes – Lemniscates (Propellers)

20. The Shapes - Spirals

21. The Shapes – Rose Curves n even – 2n petals n odd – n petals

22. 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.

23. 5. Now change the constraints in WINDOW

24. Finding Points of Intersection (Boundaries of Integration)

25. WRONG ANSWER It’s usually better to graph it first.