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: 32

Answer

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

Work Step by Step

RECALL: (1) The sine function is an odd function, which means $\sin{(-x)} = -\sin{x}$ for all numbers in its domain. (2) $\csc{x} = \dfrac{1}{\sin{x}}$ Therefore, $\csc{(-x)} \\=\dfrac{1}{\sin{(-x)}} \\=\dfrac{1}{-\sin{x}} \\=-\dfrac{1}{\sin{x}} \\=-\csc{x}$ Thus, $\csc{(-x)} = -\csc{x}$
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