Question

How do you graph `r=3sintheta`?

Answer 1

`x^2+y^2=3y`

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=3sintheta` can be written as `r^2=3rsintheta` i.e.

`x^2+y^2=3y`, which is the equation of a circle.
graph{x^2+y^2=3y [-5.375, 4.625, -0.54, 4.46]}