Question

How do you graph `r=2+2sintheta`?

Answer 1

`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]}