Question

What is the name of the shape graphed by the function `r =1+3 sin theta`?

Answer 1

It is called a Limacon, French for snail.

Explanation:

Limacons were studied by Pascal.

Answer 2

Limaçon

Explanation:

Consider the following shapes for polar graphs:

Cardiod:
`r=a+-bcostheta` and `r=a+-bsintheta`
where `a=b`

Limaçon:
`r=a+-bcostheta` and `r=a+-bsintheta`
where `a!=b`

Rose Curve:
`r=acos(ntheta)` and `r=asin(ntheta)`
if `n` is odd, then `n` petals
if `n` is event, then `2n` petals

Lemniscate
`r^2=a^2cos(2theta)` and `r^2=a^2sin(2theta)`

Based on this list, we can determine that the given polar equation is a Limaçon