Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 7 - Exponential Functions - 7.8 Inverse Trigonometric Functions - Preliminary Questions - Page 374: 3


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Work Step by Step

Two angles are complementary when they add up to 90 degrees. Thus the geometric interpretation of the identity $$\sin^{-1}x+\cos^{-1}x=\frac{\pi}{2}$$ means that $\sin^{-1}x$ and $\cos^{-1}x$ are complementary. Also, we have $$\sin^{-1}x=\frac{\pi}{2}-\cos^{-1}x$$ and this leads to $$(\sin^{-1}x)'=-(\cos^{-1}x)'.$$
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