1. GRAPHS OF THE POLAR EQUATIONS r = a ± b cos θ r = a ± b sin θ

2. HOW THE SIZES OF a, b IMPACT THE GENERAL SHAPE OF THE GRAPH r = a ± b cos θ r = a ± b sin θ

3. CIRCLE r = a + b cos θ, where |a|=0 r = 2 cos θ

4. LIMACON WITH LOOP r = a + b cos θ, where |a|<|b| r = 1 + 2 cos θ

5. CARDIOID r = a + b cos θ, where |a|=|b| r = 2 + 2 cos θ

6. LIMACON WITH DIMPLE r = a + b cos θ, where |b|<|a|<2|b| r = 3 + 2 cos θ

7. CONVEX LIMACON r = a + b cos θ, where |a|=2|b| r = 4 + 2 cos θ

8. CONVEX LIMACON r = a + b cos θ, where |a|>2|b| r = 5 + 2 cos θ

9. HOW THE TRIGONOMETRIC FUNCTION IMPACTS THE ORIENTATION OF THE GRAPH r = a ± b cos θ r = a ± b sin θ

10. r = a + b cos θ, where a > 0, b > 0 r = 1 + 2 cos θ

11. r = a + b sin θ, where a > 0, b > 0 r = 1 + 2 sin θ

12. HOW THE SIGNS OF a, b IMPACT THE DIRECTION OF THE GRAPH r = a ± b cos θ r = a ± b sin θ

13. r = a + b cos θ, where a > 0, b > 0 r = 1 + 2 cos θ

14. r = a + b cos θ, where a > 0, b < 0 r = 1 - 2 cos θ

15. r = a + b cos θ, where a < 0, b > 0 r = -1 + 2 cos θ

16. r = a + b cos θ, where a < 0, b < 0 r = -1 - 2 cos θ

17. PUTTING IT TOGETHER GUESS THE GRAPH BY DETERMINING THE SHAPE, THE ORIENTATION & THE DIRECTION r = sin θ

18. r = sin θ

19. PUTTING IT TOGETHER GUESS THE GRAPH BY DETERMINING THE SHAPE, THE ORIENTATION & THE DIRECTION r = cos θ

20. r = cos θ

21. GRAPHS OF THE POLAR EQUATIONS r = a cos nθ r = a sin nθ

22. HOW THE VALUE OF n IMPACTS THE GENERAL SHAPE OF THE GRAPH r = a cos nθ r = a sin nθ

23. r = 3 cos θ

24. r = 3 cos 2θ

25. r = 3 cos 3θ

26. r = 3 cos 4θ

27. r = 3 cos 5θ

28. r = 3 cos 6θ

29. HOW THE TRIGONOMETRIC FUNCTION IMPACTS THE ORIENTATION OF THE GRAPH r = a cos nθ r = a sin nθ

30. r = 3 cos θ

31. r = 3 sin θ

32. r = 3 cos 2θ

33. r = 3 sin 2θ

34. r = 3 cos 3θ

35. r = 3 sin 3θ

36. r = 3 cos 4θ

37. r = 3 sin 4θ

38. r = 3 cos 5θ

39. r = 3 sin 5θ

40. r = 3 cos 6θ

41. r = 3 sin 6θ

42. PUTTING IT TOGETHER GUESS THE EQUATION OF A ROSE CURVE WITH [a] 16 petals [b] 15 petals [c] 14 petals