6.5: Graphing Polar Equations 1. y = cosx 2. y = sinx€¦ · Limacon Curves: r = a + b cos θ r =...
Transcript of 6.5: Graphing Polar Equations 1. y = cosx 2. y = sinx€¦ · Limacon Curves: r = a + b cos θ r =...
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6.5: Graphing Polar Equations
1. y = cosx 2. y = sinx
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r = cosθ
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r = sinθ
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y = 3cos θ
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Algebraic Relationship
r = cos O
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r = sin O
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Symmetry:
1. line O =
2. polar axis
3. the pole
(r,θ)
(r,θ)
(r,θ)
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Use polar symmetry tests to determine if the graph is symmetric about the x-axis, the y-axis, or the origin.
r = 4 sin 3θ
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Find the maximum r-value of the following graphs.
1. r = 3 + 2cos θ 2. r = 4 - sin θ
Maximum r-value: value occurring at a point the maximum distance from the pole.
*To find: find values of |r| as opposed to the directed distance r.
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Analyze the graph of the polar curve.
r = -3 cos 4θ
Domain:___________________Range:____________________Continuity:_________________Boundedness: ______________Symmetry: ________________Maximum r-value: ___________Asymptotes:_______________
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Rose Curves: r = a cos nθr = a sin nθ
Limacon Curves: r = a + b cos θr = a + b sin θ
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Lemniscates: r2 = a2sin 2θ
r2 = a2cos 2θ
Spiral of Archimedes: r = θ
where n is an integer > 1
n is even: 2n petalsn is odd: n petals
r-value max = a + b
where a > 0, b > 0