A Problem with 60 Degree Angle Trigonometry

I have rediscovered a problem with 60° angle trigonometry. The problem is that arccos(a) and arcsin(b) for this trigonometry are not functions. In the following drawing, A and C are points on a unit circle with center B. θ is the measure of the angle ABC. The measure of the angle CAB is 60°. The value returned by arccos(1) would validly be both zero and θ, as in the drawing. Similarly, the value returned by arcsin(1) would validly be both θ and 120°.