Trigonometry: Determine 'Polar Coordinates' of Given 'Cartesian Coordinates' |?

You are making this way too complicated. The angle is in Quadrant III, SAME as the (x,y) point. Yes, arctan(7/6) gives you 49.4° or .86 radians, but those angles are in Quadrant I. Just add 180° or π radians to get the angle in the third quadrant with the same tangent.