Question

How do you graph `r= 5 sin theta`?

Answer 1

`x^2+y^2-5y=0`

Explanation:

The relation between polar coordinates `(r,theta)` and rectangular Cartesian coordinates `(x,y)` are given by

`x=rcostheta` and `y=rsintheta` or `r^2=x^2+y^2`

Hence `r=5sintheta` can be written as

`r^2=5rsintheta`

or `x^2+y^2=5y`

or `x^2+y^2-5y=0`