Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 5 - Trigonometric Identities - Section 5.1 Fundamental Identities - 5.1 Exercises - Page 202: 83


$sin~x = \sqrt{1-cos^2~x}~~~~$ is not an identity.

Work Step by Step

The graph of $sin~x$ includes both positive and negative values on the vertical axis. However, the graph of $\sqrt{1-cos^2~x}$ does not include any negative values on the vertical axis. For example, $sin (\frac{3\pi}{2}) = -1$ but $\sqrt{1-cos^2~(\frac{3\pi}{2}}) = 1$ Therefore, $~~sin~x = \sqrt{1-cos^2~x}~~~~$ is not an identity.
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