Trigonometry (11th Edition) Clone

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

Chapter 4 - Graphs of the Circular Functions - Section 4.4 Graphs of the Secant and Cosecant Functions - 4.4 Exercises - Page 180: 37


$\sec{(-x)} = \sec{x}$. Please refer to the step-by-step part for the complete solution.

Work Step by Step

RECALL: (1) The cosine function is an even function, which means $\cos{(-x)} = \cos{x}$ for all numbers in its domain. (2) $\sec{x} = \dfrac{1}{\cos{x}}$ Therefore, $\sec{(-x)} \\=\dfrac{1}{\cos{(-x)}} \\=\dfrac{1}{\cos{x}} \\=\sec{x}$ Thus, $\sec{(-x)} = \sec{x}$
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