Why doesn't $\arccos x = -\tfrac12\sqrt{3}$ have any solutions? I have this exercise with an unclear answer. The question is this:
$$\arccos x = -\frac{\sqrt3}{2}\,.$$
The answer is this:
$$\begin{gather*}
\varphi(x)= \arccos x\\
V_\varphi = [0,\pi]\\
-\frac{\sqrt3}{2}\notin V_\varphi\,.
\end{gather*}
$$
can someone this a bit more to me? How does this prove that there are no solutions?

Domain of $\arccos(x)$ is $[-1,1]$ (not $\mathbb{R})$, so the range of values is $[0,\pi]$, but $\frac{-\sqrt{3}}{2}<0$, so it isn't in range.
