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

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±bcosθ and r=a±bsinθ
where a=b

Limaçon:
r=a±bcosθ and r=a±bsinθ
where ab

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

Lemniscate
r2=a2cos(2θ) and r2=a2sin(2θ)

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