# 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# petalsLemniscate

#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**