yes, but cos inverse 1 also equals 2pi, so how do you know which one to use?

for the second one, my question was how do you then isolate x from your last line?

This red bit is

**not true**.

\[ \text{The function }f(x) = \cos^{-1}x\text{ has range }0\leq y \leq \pi.\\ \text{The value it returns }\textbf{must}\text{ be a value associated with the first or second quadrant.} \]

Note that the \(x\) can also be isolated in the second equation by brute force: \(\displaystyle2x = 2n\pi \pm \frac\pi2 - \frac\pi4 \implies \boxed{x=n\pi \pm \frac\pi4 - \frac\pi8}\). Although I would favour fun_jirachi's answer over this notation.