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: 21


$-\displaystyle \frac{\pi}{3}$

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 $y=-\displaystyle \frac{\pi}{3}$ such that $\displaystyle \sin(-\frac{\pi}{3}) =-\displaystyle \frac{\sqrt{3}}{2}$ so $y=$ arcsin$(-\displaystyle \frac{\sqrt{3}}{2})=-\frac{\pi}{3}$
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