Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 7 - Trigonometric Identities and Equations - 7.5 Inverse Circular Functions - 7.5 Exercises: 3

Answer

Fill the blank with ... $\cos y$ ...

Work Step by Step

When we restrict the domain of $\cos x$ to $[0,\pi]$, it becomes one-to-one and has an inverse. For inverse functions, $f(f^{-1}(y))=y$ and $f^{-1}(f(x))=x.$ So, with $\cos^{-1}x$ being the inverse of $\cos x$ (on the restricted domain), $\cos y=\cos[\cos^{-1}(x)]=x.$ Fill the blank with ... $\cos y$ ...
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