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: 6

Answer

The domain is all real numbers except $\theta=(2k+1)\cdot\frac{\pi}{2}$, where $k$ is an integer.

Work Step by Step

The denominator cannot be 0, hence $cos(\theta)$ cannot be 0. $cos(\theta)=0$ if and only if $\theta=(2k+1)\cdot\frac{\pi}{2}$, where $k$ is an integer. Therfore the domain is all real numbers except $\theta=(2k+1)\cdot\frac{\pi}{2}$, where $k$ is an integer.
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