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Hint

1

acosθ or asinθ

circle

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2

acos(nθ) or asin(nθ)

polar rose; if n is odd, it will have n amount of petals. if n even —> 2n amount of petals

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3

a +(-) bcosθ or a +(-)bsinθ when b is not equal to a

limacon; if b > a —> loop, if b < a —> no loop.

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4

a +(-) bcosθ or a +(-)bsinθ when b is equal to a

cardioid

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5

θ = k

linear equation with a slope of k and passes through origin

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6

rcosθ =a or rsinθ =a

vertical/horizontal line at a

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7

r² = a² cos2θ or r² = a² sin2θ

lemniscates; cos is horizontal while sin is diagonal

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8

r = aθ

archimedean spiral

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