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There was a question on my math test that asked for the principal value of $\arcsin(\sin(10)$. My friend says it is $10-3 \pi$ but I say it is $3 \pi -10$. However, taking into account the definition of the range of the inverse sin function, couldnt it be either? Since the answer $A$ has to be such that $\frac{\pi}{2}.

Can someone clarify this?

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    It is $3 \pi - 10$ as you say it.2011-09-24
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    $\sin(3\pi-10)=-\sin(10-3\pi)$, so a simple calculation of the sine values should show that one of the two proposed answers must be wrong.2011-09-24

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