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?