1. 8. Polar Coordinates I am the polar curve r = sin(2^t)-1.7

2. Polar Coordinates EQ – How do you graph polar equations?

3. One way to give someone directions is to tell them to go three blocks East and five blocks South. Another way to give directions is to point and say “Go a half mile in that direction.” Polar graphing is like the second method of giving directions. Each point is determined by a distance and an angle. Initial ray A polar coordinate pair determines the location of a point. Polar Graphing

4. (Circle centered at the origin) (Line through the origin) Some curves are easier to describe with polar coordinates:

5. Polar Equations To convert from polar coordinates to rectangular coordinates, you need to know that

6. Example Convert to rectangular coordinates

7. Polar Equations To convert from rectangular coordinates to polar coordinates, you need to know that

8. Example Convert to polar coordinates

9. Example Convert to a rectangular equation

10. Example Convert to a rectangular equation

11. Example Convert to a rectangular equation

12. Example Convert to a polar equation

13. Finding where a graph crosses the origin (the pole) Set equation equal to 0 and solve Example

14. Lines Polar Rectangular

15. Lines Polar Rectangular

16. Lines Polar Rectangular

17. Example Graph

18. Circles Polar Rectangular Center is at origin, a is radius

19. Circles Polar Rectangular Center is at (a,b), radius is

20. Example Graph Center is at (5/2,4), radius is = 4.7

21. Cardioids Heart shaped, include origin http://www.intmath.com/plane-analytic- geometry/8-curves-polar-coordinates.php

22. Limacon When a<b, have inner loop, include origin

23. Roses If n is even, rose has 2n petals, if n is odd, rose has n petals

24. Lemniscate Looks like an infinity sign, length is a Sin is diagonal

25. Assignment Pg. 645: #3-7 odd, 8, 9, 10, 11-21 odd, 22, 25