types of polar graphs - precalc

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5 Terms

1
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circles

r = asinθ (up/down) or r = acosθ (left/right)

a > 0 - right/up

a < 0 left/down

2
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limacons

r = a + bcosθ or r = a + bsinθ (a and b +)

inner loop - a < b (a - bsinθ)

cardioid - a = b (a +bcosθ)

dimpled limacon - b < a < 2b (a - bcosθ)

convex limacon a ≥ 2b (a + bsinθ)

3
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roses

n petals - n odd

2n petals - n even

4 petals - asinnθ

3 petals - asinnθ

8 petals - acosnθ

5 petals - acosnθ

<p>n petals - n odd</p><p>2n petals - n even</p><p>4 petals - asinnθ</p><p>3 petals - asinnθ</p><p>8 petals - acosnθ</p><p>5 petals - acosnθ</p>
4
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leminscates

<p></p>
5
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spiral of archimedes

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