The general form for a limacon is $r = a + b cos θ$ $r=a+bcostheta$ or $r = a + b sin θ$ $r=a+bsintheta$ . When will a limacon have a dimple?

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Answer 1 · 2018-04-08T16:31:09

Please see below.

Observe that we can write $r = a + b cos θ$ $r=a+bcostheta$ as

$r = a + b sin (\frac{π}{2} - θ)$ $r=a+bsin(pi/2-theta)$

Hence, there is not much of a difference and either can represent a limacon. However, general form used is $r = a + b cos θ$ $r=a+bcostheta$ .

If the equation is $r = a + b cos θ$ $r=a+bcostheta$

Limacon will have a dimple if $b < a < 2 b$ $b < a < 2b$

Additional Information - Limacon will have inner loop if $b = 2 a$ $b=2a$

The general form for a limacon is r=a+bcosθr=a+bcostheta or r=a+bsinθr=a+bsintheta. When will a limacon have a dimple?