Question

what is the name of the polar graph
r=1+sin(theta) and a characteristic?

Answer 1

This is known as a cardioid (since it looks somewhat like a heart). It's defining characteristic is that it's mostly circular but has a cusp on it that gives it its heart-like feature.

http://en.wikipedia.org/wiki/Cardioid

Answer 2

shweet thanks

Answer 3

Graph can be seen here

http://www.wolframalpha.com/input/?i=polar+plot+r%3D1%2Bsin%28theta%29