fill in each blank so that the resulting statement is true. by restricting the domain of y = sin x to _, the…

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 -\\frac{\\pi}{2}\\leq x\\leq\\frac{\\pi}{2}, the restricted sine function has an inverse function. the inverse sine function is denoted by y = _

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 -\\frac{\\pi}{2}\\leq x\\leq\\frac{\\pi}{2}, the restricted sine function has an inverse function. the inverse sine function is denoted by y = _

Answer

Explanation:

Step1: Recall inverse sine notation

The inverse sine function is denoted as $y = \sin^{-1}x$ or $y=\arcsin x$.

Step2: Recall domain for inverse - sine

The sine function $y = \sin x$ is one - to - one (and thus has an inverse) when its domain is restricted to $\left[-\frac{\pi}{2},\frac{\pi}{2}\right]$.

Answer:

First blank: $\sin^{-1}x$ (or $\arcsin x$) Second blank: $\left[-\frac{\pi}{2},\frac{\pi}{2}\right]$