Question

How do you find the polar coordinates of the point with rectangular coordinates `(-2,2` )?

Answer 1

The rectangular coordinates `(x,y)=(-2,2)` are `(r,theta)=(2sqrt{2},{3pi}/4)` in polar coordinates.

Since `r` is the distance of the point from the origin,

`r-sqrt{x^2+y^2}=sqrt{(-2)^2+2^2}=sqrt{8}=2sqrt{2}`

Since the positive x-axis and the segment connecting the origin and the point make `135^circ={3pi}/4` rad,

`theta={3pi}/4`