Question

Tips and answer to finding principal value

Answer 1

X =\[\sin^{-1} (\sqrt{2}/2)\]

Answer 2

look at a cheat sheet if you do not remember which angle (number) has sine of
\[\frac{\sqrt{2}}{2}\]
you will see that it is
\[\frac{\pi}{4}\] and although there are infinitely many others, this is the only one in the interval
\[[-\frac{\pi}{2},\frac{\pi}{2}]\]