Today in Precalculus Go over homework Notes: Graphs of Polar Equations Homework

Rose Curves 1. r = 4sin3θ 2. r = 4cos3θ 3. r = 4sin2θ4. r = 4cos2θ

Conclusions General form of the equations: r = acosnθ r = asinnθ Number of petals: if n is odd, n petals if 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 axis sin: 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 Curves 5. r = 2 – 3sinθ 6. r = 2 + 2sinθ 7. r = 3 + 2cosθ8. r = 2 – 1cosθ

Conclusions General form of the equations: r = a ± bcosθ r = a ± bsinθ

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 = 4sin3 θ Domain: All reals Range: [-4, 4] Maximum r-value: 4 Symmetry: y-axis Continuity: continuous Boundedness: bounded Asymptotes: none

r = 4cos3 θ Domain: All reals Range: [-4, 4] Maximum r-value: 4 Symmetry: x-axis Continuity: continuous Boundedness: bounded Asymptotes: none

r = 2 – 3sin θ Domain: All reals Range: [-1, 5] Maximum r-value: 5 Symmetry: y-axis Continuity: continuous Boundedness: bounded Asymptotes: none

r = 2 +2sin θ Domain: All reals Range: [0, 4] Maximum r-value: 4 Symmetry: y-axis Continuity: continuous Boundedness: bounded Asymptotes: none

r = 3 +2cos θ Domain: All reals Range: [1,5] Maximum r-value: 5 Symmetry: x-axis Continuity: continuous Boundedness: bounded Asymptotes: none

r = 2 – 1cos θ Domain: All reals Range: [1,3] Maximum r-value: 3 Symmetry: x-axis Continuity: continuous Boundedness: bounded Asymptotes: none

Homework Worksheet Quiz Monday, April 13