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 487: 130a


The identity is verified. $arcsin(-x)=-arcsin~x$

Work Step by Step

Let $x=sin~y$, then $y=arcsin~x$. We know that $sin(-y)=-sin~y$ because $sin~y$ is odd. So, $-x=sin(-y)$. Then: $arcsin(-x)=-y=-arcsin~x$
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