How do you determine the shape of a limaçon from the polar equation?

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How do you determine the shape of a limaçon from the polar equation?

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Answer 1 · 2015-04-13T18:29:34

A polar graph that is a limacon has a formula similar to $r = a \pm b cos θ$ $r= a +- bcostheta$ or $r = a \pm b sin θ$ $r= a +- bsintheta$
where $a < b$ $a<b$ or $a > b$ $a>b$

Case1: $a < b$ $a<b$
Here you have a limacon with an inner loop
Example: $r = 2 + 4 cos θ$ $r = 2 + 4costheta$

Case2: $a > b$ $a>b$
In this case, the limacon does not have an inner loop.
Example: $r = 5 + cos θ$ $r = 5 + costheta$

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How do you determine the shape of a limaçon from the polar equation?

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