Polar Equations Precalc

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19 Terms

1
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r = A

Circle along origin, A = radius

2
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r = Asinθ

Circle along y-axis, A = radius

3
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r = Acosθ

Circle along x-axis, A = radius

4
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r = AsinBθ

Rose curve spaced throughout 360, A = radius, B = # petals

5
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r = AcosBθ

Rose curve spaced along axis A = radius, B = # petals

6
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Rose curve with even B

# petals = 2B, 180 degrees for full graph

7
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Rose curve with odd B

# petals = B, 360 degrees for full graph

8
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Loop Limacon

A / B < 1

9
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Cardioid

A / B = 1

10
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Dimpled Limacon (worse heart)

1 < A / B < 2

11
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Convex Limacon (oval)

A / B >= 2

12
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r = A ± Bcosθ

Limacon curve, a = y-int, rmax = furthest x

13
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r = A ± Bsinθ

Limacon curve, a = x-int, rmax = furthest y

14
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A in limacon curve (r = A ± Bsinθ)

A = (Rmax + Rmin) / 2

15
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B in limacon curve (r = A ± Bsinθ)

B = (Rmax - Rmin) / 2

16
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r² = A²sin2θ

Leminscate equation, A = radius, rotated 45/45

17
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r² = A²cos2θ

Leminscate equation, A = radius, along x-axis

18
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r = Aθ

Archimedes spiral

19
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R = A / θ

Reciprocal spiral