Types of Polar Graphs

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Last updated 3:18 AM on 6/16/26
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16 Terms

1
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Graph of r = a

Circle centered at the pole with a radius of |a|

<p>Circle centered at the pole with a radius of |a|</p>
2
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Graph of r = acosθ

Circle centered on the line θ = 0, |a|/2 units from the pole, radius = |a|/2

<p>Circle centered on the line θ = 0, |a|/2 units from the pole, radius = |a|/2</p>
3
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Graph of r = asinθ

Circle centered on line θ = π/2, |a|/2 units from pole, radius = |a|/2

<p>Circle centered on line θ = π/2, |a|/2 units from pole, radius = |a|/2</p>
4
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Graph of r = a ± bsinθ if a/b = 1

Cardioid, centered on line θ = π/2

<p>Cardioid, centered on line θ = π/2</p>
5
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Graph of r = a ± bcosθ if a/b = 1

Cardioid, centered on line θ = 0

<p>Cardioid, centered on line θ = 0</p>
6
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Graph of r = a ± bsinθ if a/b < 1

Limacon with an inner loop, centered on line θ = π/2

<p>Limacon with an inner loop, centered on line θ = π/2</p>
7
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Graph of r = a ± bcosθ if a/b < 1

Limacon with an inner loop, centered on line θ = 0

<p>Limacon with an inner loop, centered on line θ = 0</p>
8
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Graph of r = a ± bsinθ if 1 < a/b < 2

Limacon with a dimple, centered on line θ = π/2

<p>Limacon with a dimple, centered on line θ = π/2</p>
9
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Graph of r = a ± bcosθ if 1 < a/b < 2

Limacon with a dimple, centered on line θ = 0

<p>Limacon with a dimple, centered on line θ = 0</p>
10
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Graph of r = a ± bsinθ if a/b ≥ 2

Convex limacon with no inner loop or dimple, centered on line θ = π/2

<p>Convex limacon with no inner loop or dimple, centered on line θ = π/2</p>
11
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Graph of r = a ± bcosθ if a/b ≥ 2

Convex limacon with no inner loop or dimple, centered on line θ = 0

<p>Convex limacon with no inner loop or dimple, centered on line θ = 0</p>
12
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Graph of r=asinnθ where n is odd

Rose, n petals

<p>Rose, n petals</p>
13
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Graph of r=asinnθ where n is even

Rose, 2n petals,

<p>Rose, 2n petals,</p>
14
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Graph of r=acosnθ where n is odd

Rose, n petals,

<p>Rose, n petals,</p>
15
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Graph of r=acosnθ where n is even

Rose, 2n petals,

<p>Rose, 2n petals,</p>
16
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Graph of r = aθ

Spiral

<p>Spiral</p>