How do you graph r=2+2sintheta?

1 Answer
Jan 4, 2017

x^2+y^2=4(1+y^2/(x^2+y^2)+2y/sqrt(x^2+y^2))

Explanation:

The relation between polar coordinates (r,theta) and Cartesian coordinates (x,y) is

x=rcostheta and y=rsintheta i.e. r^2=x^2+y^2 and y/x=tantheta

Hence r=2+2sintheta can be written as

sqrt(x^2+y^2)=2(1+sintheta)

or x^2+y^2=4(1+y/sqrt(x^2+y^2))^2

or x^2+y^2=4(1+y^2/(x^2+y^2)+2y/sqrt(x^2+y^2))
graph{x^2+y^2=4(1+y^2/(x^2+y^2)+2y/sqrt(x^2+y^2)) [-5.21, 4.79, -0.76, 4.24]}