Answer
$arccos(\frac{\sqrt 2}{2})=\frac{\pi}{4}$
Work Step by Step
The range of $arccos~x$ is $[0,\pi]$. So,
$arccos(\frac{\sqrt 2}{2})=\frac{\pi}{4}$, because $cos(\frac{\pi}{4})=\frac{\sqrt 2}{2}$ and $0\leq\frac{\pi}{4}\leq\pi$
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