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

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Presentation on theme: "GRAPHS OF THE POLAR EQUATIONS r = a ± b cos θ r = a ± b sin θ."— Presentation transcript:

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 = cos θ

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

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

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

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

11 r = a + b sin θ, where a > 0, b > 0 r = 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 = cos θ

14 r = a + b cos θ, where a > 0, b < 0 r = cos θ

15 r = a + b cos θ, where a 0 r = cos θ

16 r = a + b cos θ, where a < 0, b < 0 r = cos θ

17 HOW WOULD YOU FIND THE x- AND y-INTERCEPTS OF A POLAR CURVE r = f(θ) ?

18 FIND THE VALUES OF r FOR θ = 0, π/2, π AND 3π/2 BE CAREFUL OF NEGATIVE VALUES OF r (THE INTERCEPTS WILL APPEAR ON THE OPPOSITE SIDE OF THE AXIS)

19 1.Determine the shape of the graph by comparing |a| to |b| and 2|b| 2.Determine the axis of symmetry from the trigonometric function 3.Determine the direction of the fat part from the sign of the trigonometric function 4.Find and plot the x- and y-intercepts by finding the values of r for = 0, π/2, π AND 3π/2 5.Connect and form the appropriate shape Circles, cardioids and limacons with loops pass through the pole; dimpled and convex limacons do not GRAPHS OF THE POLAR EQUATIONS r = a ± b cos θ r = a ± b sin θ

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

21 r = sin θ

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

23 r = cos θ

24 GRAPHS OF THE POLAR EQUATIONS r = a cos nθ r = a sin nθ

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

26 r = 3 cos θ

27 r = 3 cos 2θ

28 r = 3 cos 3θ

29 r = 3 cos 4θ

30 r = 3 cos 5θ

31 r = 3 cos 6θ

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

33 PUTTING IT TOGETHER [a] r = a sin 8θ or r = a sin 8θ [b] r = a sin 15θ or r = a sin 15θ [c] no such rose curve

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

35 r = 3 cos θ

36 r = 3 sin θ

37 r = 3 cos 2θ

38 r = 3 sin 2θ

39 r = 3 cos 3θ

40 r = 3 sin 3θ

41 r = 3 cos 4θ

42 r = 3 sin 4θ

43 r = 3 cos 5θ

44 r = 3 sin 5θ

45 r = 3 cos 6θ

46 r = 3 sin 6θ


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