Chapter 6.CR, Problem 10CC

(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 $\mathrm{s}\mathrm{i}\mathrm{n}({\sin }^{-1}x)=x$ true? For what values of $x$ is the equation ${\sin }^{-1}(\sin x)=x$ true?