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: 38


$\csc{(-x)} = -\csc{x}$. 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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