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: 97


odd multiples of $\dfrac{\pi}{2}$

Work Step by Step

Since $\tan(\theta)=\dfrac{\sin\theta}{\cos\theta}$, then it is undefined when the denominator (which is $\cos{\theta}$) is $0$. Recall that $\cos\theta=0$ if $\theta=\frac{\pi}{2}(2k+1)$, where $k$ is an integer. Therefore, the tangent function is undefined when $\theta=\frac{\pi}{2}(2k+1)$, where $k$ is an integer (which are odd multiples of $\frac{\pi}{2}$).
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