Polar coordinates representing two points.

Question

The polar coordinates of a point are [5,tan inverse(3/4)-180°]. But tan inverse (3/4)-180° = either -143.13° or 36.869° as tan(180+A)=tanA. How a single polar coordinate can represent two points in the plane?

Answer 1

It can only represent one point on the plane. You just mentioned that $\tan(\theta+180º)=\tan(\theta).$

That means two points exactly opposite from each other will have the same value of $\tan(\theta)$.

$\arctan(\theta)$ only identifies angles between $-90º$ and $90º$.

If we know that the point falls in quadrant II or quadrant III, we need to add $180º$ to our angle.