Question

How do you convert `(0, −4)` into polar form?

Answer 1

The polar coordinates are `(4,(3pi)/2)`

Explanation:

Use the definition
`x=rcostheta`
`y=rsintheta`
`x^2+y^2=r^2`

`tantheta=y/x`

where `(x,y)`are the cartesian coordinates
and `(r,theta)`are the polar coordinates
Here we have `tantheta=-4/0=-oo`
So `theta=(3pi)/2`
and `r^2=0+16` `=>` `r=4`
So the polar coordinates are `(4,(3pi)/2)`