If a motor spins in the reverse direction and completes 1/8 of a revolution what angle will the resolver output? The angle that the resolver measures should be -pi/4 However if it only treats angles as positive then it would measure pi/4. But pi/4 and -pi/4 are completely different motor positions? How does the resolver distinguish between positive and negative angles?
First, resolvers don't care about positive and negative. The two outputs are sine waves at the reference frequency (classically 400 Hz), amplitude modulated with the sine and cosine of the shaft angle.
Standard resolver-to-digital decoder modules produce a binary word which varies from 0...0 to F...F over 360 degrees (or 2pi radians, take your pick). How you treat this number (0 to 2 pi, or -pi to pi) is entirely up to you.
Assuming a 0 to 2 pi representation, the second angle will not be interpreted as -pi/4, but rather as 1.75 pi. Of course, you are free to add whatever offsets you like.