polar equation graphs

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Calculus

Parametric Equations & polar Coordinates

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8 Terms

1
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acosθ or asinθ

circle

<p>circle</p>
2
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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

<p>polar rose; if n is odd, it will have n amount of petals. if n even —&gt; 2n amount of petals</p>
3
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a +(-) bcosθ or a +(-)bsinθ when b is not equal to a

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

<p>limacon; if b &gt; a —&gt; loop, if b &lt; a —&gt; no loop.</p>
4
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a +(-) bcosθ or a +(-)bsinθ when b is equal to a

cardioid

<p>cardioid</p>
5
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θ = k

linear equation with a slope of k and passes through origin

<p>linear equation with a slope of k and passes through origin</p>
6
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rcosθ =a or rsinθ =a

vertical/horizontal line at a

<p>vertical/horizontal line at a</p>
7
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r² = a² cos2θ or r² = a² sin2θ

lemniscates; cos is horizontal while sin is diagonal

<p>lemniscates; cos is horizontal while sin is diagonal</p>
8
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r = aθ

archimedean spiral

<p>archimedean spiral</p>