Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 6 - Trigonometric Functions - 6.5 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions - 6.5 Assess Your Understanding - Page 418: 14

Answer

$x=-2\pi,-\pi,0,\pi,2\pi$, $\csc{x}=\frac{1}{\sin{x}}$

Work Step by Step

If $x=-2\pi,-\pi,0,\pi,2\pi$, $\csc{x}=\frac{1}{\sin{x}}$ has vertical asymptotes because $\sin{x}=0$ at those values, hence the denominator is $0$, therefore $\csc{x}$ is undefined at those values. (see graph)
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