Since the cosine function is not one-to-one, its inverse would not be a
function.  So cos-1(x) was defined so that it would be a function by
restricting its domain to [0,p] or {y|0≦y≦p}, which is never negative.
Therefore by definition cos-1(-0.9) is between 0 and p, actually in 
quadrant II between  and p, approximately 2.69 (radians).
Edwin