Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 5 - Section 5.5 - Inverse Trigonometric Functions and Their Graphs - 5.5 Exercises - Page 445: 33


$\Rightarrow \sin ^{-1}\left( \sin \left( \dfrac {3\pi }{4}\right) \right) =\sin ^{-1}\left( \sin \left( \dfrac {\pi }{4}\right) \right) =\dfrac {\pi }{4}$

Work Step by Step

$\sin ^{-1}\left( \sin x\right) =x\left( -\dfrac {\pi }{2}\leq x\leq \dfrac {\pi }{2}\right) $ $\dfrac {3\pi }{4} > \dfrac {\pi }{2}$ so we need to convert it $ \sin \dfrac {3\pi }{4}=\sin \dfrac {\pi }{4}$ $\Rightarrow \sin ^{-1}\left( \sin \left( \dfrac {3\pi }{4}\right) \right) =\sin ^{-1}\left( \sin \left( \dfrac {\pi }{4}\right) \right) =\dfrac {\pi }{4}$
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