Question

How do you convert the cartesian coordinate (-5, -5) into polar coordinates?

Answer 1

`(r,theta)=(5sqrt(2),(5pi)/4)`

Explanation:

For `r`, use the formula `r=sqrt(x^2+y^2)=sqrt(5^2+5^2)=sqrt(50)=sqrt(25)sqrt(2)=5sqrt(2)`.

For `theta`, note that the point `(x,y)=(-5,-5)` is in the third quadrant. Hence, `theta=tan^{-1}(y/x)+pi=tan^{-1}(1)+pi=pi/4+pi=(5pi)/4` (adding or subtracting any whole number multiple of `pi` to this also works for `theta`).