Precalculus (10th Edition)

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

Chapter 6 - Trigonometric Functions - 6.3 Properties of the Trigonometric Functions - 6.3 Assess Your Understanding - Page 395: 100


$\theta=k\pi$, where k is an integer

Work Step by Step

Since $\csc(\theta)=\frac{1}{\sin\theta}$, then it is undefined when the denominator (which is $\sin{\theta}$) is $0$. Recall that $\sin\theta=0$ if $\theta=k\pi$, where $k$ is an integer. Therefore, the function is undefined when $\theta=k\pi$, where k is an integer.
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