Question

The cartesian coordinates of a point are given. find polar coordinares of the point where r<0 and

Answer 1

Find the polar coordinates in the usual way, then negate r and add 180° to θ.

You know that

... r = √(x² + y²)

... θ = arctan(y/x) . . . . . taking quadrant into account

The coordinates (r, θ) and (-r, θ+180°) specify the same point.