Question

How do you find the polar coordinates given `(-2,2)`?

Answer 1

Please see the explanation. The polar point is: `(2sqrt(2), (3pi)/4)`

Explanation:

Radial component is:

`r = sqrt((-2)^2 + 2^2)`

`r = sqrt(8) = 2sqrt(2)`

The x component is negative and y component is positive so we add `pi` to the inverse tangent function, to place resulting angle in the second quadrant:

`theta = tan^-1(2/-2) + pi`

`theta = -pi/4 + pi`

`theta = (3pi)/4`