Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 4 - Section 4.2 - Trigonometric Functions: The Unit Circle - Exercise Set - Page 549: 94


The function will be periodic, if it repeats its character after a certain interval of time. That is, if $f\left( x+T \right)=f\left( x \right)$ then it will be a periodic function.

Work Step by Step

Sine and cosine functions are periodic because they repeat their character after $2\pi $ , or $\begin{align} & \sin \left( x+2\pi \right)=\sin x \\ & \cos \left( x+2\pi \right)=\cos x \\ \end{align}$ So, the sine and cosine functions are periodic. Example: $\begin{align} & \sin \left( \frac{\pi }{4}+2\pi \right)=\sin \frac{\pi }{4} \\ & \cos \left( \frac{\pi }{4}+2\pi \right)=\cos \frac{\pi }{4} \\ \end{align}$
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