Is the range of arccos(x) arbitrary?

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I understand that when you take the inverse of $f(x)=\cos(x)$, you have to limit the domain to ensure that the inverse is a function. This is limiting the range of the inverse.

I understand, then, why the ranges of $\arcsin(x)$ and $\arctan(x)$ are $[-π/2,π/2]$. However, I do not understand why the range of $\arccos(x)$ is $[0,π]$. Why can’t the range be $[-π,0]$? Is this something mathematicians have arbitrarily decided? Why have they done so?

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