Question

THE FUNCTION ARCSINE CAN ALSO BE DEFINED AS?

Answer 1

The arcsine, $\sin^{-1}$, is the inverse of the $\sin$ function. This means that it takes as inputs what would usually be outputs for the $\sin$ function and produces as outputs what would usually be inputs for the $\sin$ function.

This can be particularly useful when you're trying to find an angle on a right triangle, but you've only been given the lengths of the sides. To find any angle $\theta$ in a right triangle, just take $\sin^{-1} \frac{o}{h}$, where o is the side opposite $\theta$ and h is the hypotenuse of the right triangle.