Calculus (3rd Edition)

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

Chapter 7 - Exponential Functions - 7.2 Inverse Functions - Exercises - Page 334: 3


$[-\pi/2, \pi/2]$.

Work Step by Step

The largest interval containing zero on which $ f (x) = \sin x $ is one-to-one is $[-\pi/2, \pi/2]$. After this interval, the sin function repeats (has multiple $y$ values for the same $x=\theta$ values) and hence is no longer one-to-one.
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