Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 6 - Inverse Circular Functions and Trigonometric Equations - Section 6.1 Inverse Circular Functions - 6.1 Exercises - Page 264: 22


$\displaystyle \frac{\pi}{4}$

Work Step by Step

Inverse Sine Function $y=\sin^{-1}x$ or $y=$ arcsin $x$ means that $x=\sin y$, for $-\displaystyle \frac{\pi}{2} \leq y \leq \frac{\pi}{2}$. --------- In the interval $-\displaystyle \frac{\pi}{2} \leq y \leq \frac{\pi}{2}$ we find $y=\displaystyle \frac{\pi}{4}$ such that $\displaystyle \sin(\frac{\pi}{4}) =\displaystyle \frac{\sqrt{2}}{2}$ so $y= \displaystyle \sin^{-1}(\frac{\sqrt{2}}{2})=\frac{\pi}{4}$
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