Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 4 - Graphs of the Circular Functions - Section 4.4 Graphs of the Secant and Cosecant Functions - 4.4 Exercises - Page 175: 31

Answer

$\sec{(-x)} = \sec{x}$. 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, $\sec{(-x)} = \sec{x}$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.