Question

fill in each blank so that the resulting statement is true. by restricting the domain of y = sin x to ____, the restricted sine function has an inverse function. the inverse sine function is denoted by y = ____. by restricting the domain of y = sin x to the restricted sine function has an inverse function. the inverse sine function is denoted by y =

Explanation:

The sine function \(y = \sin x\) is one - to - one (and thus has an inverse) when its domain is restricted to \(-\frac{\pi}{2}\leq x\leq\frac{\pi}{2}\). The inverse sine function is denoted as \(y=\sin^{-1}x\) or \(y = \arcsin x\).

Answer:

First blank: \(-\frac{\pi}{2}\leq x\leq\frac{\pi}{2}\)
Second blank: \(\sin^{-1}x\) (or \(\arcsin x\))