Today in Precalculus

•Go over homework•Notes: Graphs of Polar Equations•Homework

Rose Curves1. r = 4sin3θ 2. r = 4cos3θ

3. r = 4sin2θ 4. r = 4cos2θ

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Conclusions General form of the equations:

r = acosnθr = asinnθ

Number of petals: if n is odd, n petalsif n is even, 2n petals

Position of petals: cos: if n is odd, one petal on positive x-axis if n is even, petals on each axissin: if n is odd, one petal on half of y-axis if n is even, no petals on axis

Length of petal is a

Limaçon Curves5. r = 2 – 3sinθ 6. r = 2 + 2sinθ

7. r = 3 + 2cosθ 8. r = 2 – 1cosθ

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Conclusions General form of the equations:

r = a ± bcosθ

r = a ± bsinθ

when 1, there is an inner loopa

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when 1, touches the origin "cardioida

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when 1 2, called a "dimpled limacon"a

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when 2, it is a "convex limacon"a

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Analyzing polar graphs• The domain is the set of possible inputs for • The range is the set of outputs for r. The

domain and range can be read from the “trace” or “table” features on your calculator.

• The maximum r-value is the maximum distance from the pole. This can be found using trace, or by knowing the range of the function.

• Symmetry can be about the x-axis, y-axis, or origin, just as it was in rectangular equations.

• Continuity, boundedness, and asymptotes are analyzed the same way they were for rectangular equations.

r = 4sin3θDomain: All reals

Range: [-4, 4]

Maximum r-value: 4

Symmetry: y-axis

Continuity: continuous

Boundedness: bounded

Asymptotes: none

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r = 4cos3θDomain: All reals

Range: [-4, 4]

Maximum r-value: 4

Symmetry: x-axis

Continuity: continuous

Boundedness: bounded

Asymptotes: none

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r = 2 – 3sinθDomain: All reals

Range: [-1, 5]

Maximum r-value: 5

Symmetry: y-axis

Continuity: continuous

Boundedness: bounded

Asymptotes: none

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r = 2 +2sinθDomain: All reals

Range: [0, 4]

Maximum r-value: 4

Symmetry: y-axis

Continuity: continuous

Boundedness: bounded

Asymptotes: none

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r = 3 +2cosθDomain: All reals

Range: [1,5]

Maximum r-value: 5

Symmetry: x-axis

Continuity: continuous

Boundedness: bounded

Asymptotes: none

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r = 2 – 1cosθDomain: All reals

Range: [1,3]

Maximum r-value: 3

Symmetry: x-axis

Continuity: continuous

Boundedness: bounded

Asymptotes: none

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Homework

Worksheet

Quiz Monday, April 13