Google search often yields responses on stackoverflow, which can be helpful, (if understandable)

See last answer here:
https://stackoverflow.com/questions/13975745/the-fastest-way-to-get-current-quadrant-of-an-angle

The degree angle theta needs to be converted to radians, to use the Javascript Math.sin[radianAngle]. (Max removed the need to use Math. in front of sin)

if sin[theta*PI/180] >= 0 , then output is +1.

if sin[theta*PI/180] < 0 , then output is -1.

So compare does seem to be useful. The Sine provides similar benefit to using modulus of +/- angle. Javascript Modulus (%), of angle could be used instead of Sine...

- Brian