Chapter 1.7, Problem 17ES

(a) Use a calculating utility to evaluate the expressions ${\sin }^{-1}\left({\sin }^{-1}0.25\right)$ and ${\sin }^{-1}\left({\sin }^{-1}0.9\right),$ and explain what you think is happening in the second calculation.

(b) For what values of $x$ in the interval $-1\le x\le 1$ will your calculating utility produce a real value for the function ${\sin }^{-1}\left({\sin }^{-1}x\right)$ ?