The Range of arccos

arcsin uses the angles from −90° to 90°. That does not work for cosine: $\cos\left(60^{\circ}\right)$ and $\cos\left(-60^{\circ}\right)$ are both 1/2. So those angles give two answers for one input.

So arccos uses the angles from 0° to 180°, the top half of the circle. There the cosine goes from 1 down to −1 and meets each value once. So arccos is never negative. A negative input gives an angle in quadrant II: $\arccos\left(\frac{-1}{2}\right)$ is $180^{\circ}-60^{\circ}$, which is 120°.