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

2 Answers
May 13, 2017

It is called a Limacon, French for snail.

Explanation:

Limacons were studied by Pascal.

May 13, 2017

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