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Published byJair Chantry Modified over 3 years ago

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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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)

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

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 θ = 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

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

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r = sin θ

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

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r = cos θ

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

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

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r = 3 cos θ

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r = 3 cos 2θ

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r = 3 cos 3θ

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r = 3 cos 4θ

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r = 3 cos 5θ

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r = 3 cos 6θ

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

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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

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

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r = 3 cos θ

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r = 3 sin θ

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r = 3 cos 2θ

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r = 3 sin 2θ

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r = 3 cos 3θ

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r = 3 sin 3θ

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r = 3 cos 4θ

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r = 3 sin 4θ

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r = 3 cos 5θ

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r = 3 sin 5θ

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r = 3 cos 6θ

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r = 3 sin 6θ

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When trying to figure out the graphs of polar equations we can convert them to rectangular equations particularly if we recognize the graph in rectangular.

When trying to figure out the graphs of polar equations we can convert them to rectangular equations particularly if we recognize the graph in rectangular.

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