Chapter 5.CR, Problem 11CC

(a) Define the inverse sine function, the inverse cosine function, and the inverse tangent function.

(b) Find ${\sin }^{-1}\frac{1}{2},{\cos }^{-1}\frac{\sqrt{2}}{2},$ and ${\tan }^{-1}1$.

(c) For what values of $x$ is the equation $\sin \left({\sin }^{-1}x\right)=x$ true? For what values of x is the equation ${\sin }^{-1}\left(\sin x\right)=x$ true?