Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 6 - 6.6 - Inverse Trigonometric Functions - 6.6 Exercises - Page 484: 49



Work Step by Step

$\frac{9\pi}{4}$ does not lie in the range of $arcsin~x$: ($-\frac{\pi}{2}\leq x\leq\frac{\pi}{2}$). But, we know that the period of $sin~x=2\pi$ and that $\frac{9\pi}{4}=2\pi+\frac{\pi}{4}$. So: $sin(\frac{9\pi}{4})=sin(\frac{\pi}{4})$. Now, $\frac{\pi}{4}$ lies in the range of $arcsin~x$. $arcsin[sin(\frac{9\pi}{4})]=\frac{\pi}{4}$
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