Tips and answer to finding principal value

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Tips and answer to finding principal value

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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

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