Question

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

Answer 1

Please see below.

Explanation:

Observe that we can write `r=a+bcostheta` as

`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+bcostheta`.

If the equation is `r=a+bcostheta`

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

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