Question

How do you find the polar coordinate of `(3, -2)`?

Answer 1

Polar coordinates are `(3.606,-33.69^o)`

Explanation:

If rectangular coordinates are given by `(x,y)`, polar coordinates are `(r,theta)` where

`r=sqrt(x^2+y^2)` and `theta=tan^(-1)(y/x)`

Hence polar coordinates of `(3,-2)` are given by

`r=sqrt(3^2+(-2)^2)=sqrt(9+4)=3.606`

and `theta=tan^(-1)(-2/3)=-33.69^o`

Hence polar coordinates are `(3.606,-33.69^o)`