I have recangular coordinates at (1,1) and am to convert to Polar coordinates

My Problem: I thought that (1,1) was a point on the cartesian plane that described which quadrant the vector appeared in. Right 1, up 1 Quadrant-1 yes?

My book's answers show 2 solutions (which you can prove easily enough), but I though that knowing the coordinate made finding alternate solutions superfluous?

Example

(1,1) to Polar

r= sqrt(2) and tanx = (pi/4) *since in QI, then tan=pi/4 is correct

Book ALSO shows

r=+-sqrt(2) and tanx=(pi/4) or (5pi/4)

Which gives

(sqrt(2),(pi/4)) OR (-sqrt(2),(5pi/4))

If you calculate the polar coordinates back to rectangular for either answer you will indeed get (1,1) - But... why the extra work? Am I misinterpreting the implications of rectangular coordinates?

Thank you for your time