Precalculus (10th Edition)

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

Chapter 6 - Trigonometric Functions - 6.4 Graphs of the Sine and Cosine Functions - 6.4 Assess Your Understanding - Page 409: 59


$y=3\sin(\pi x).$

Work Step by Step

If a function has form $y=A\sin(\omega x)$, then there $|A|$ stands for the amplitude and $T =\frac{2\pi}{\omega}$ stands for the period. First we identify $\omega$ and $A$ and then plug them into the form of $y=A\sin(\omega x)$. Hence $A=|3|=3$, $\omega=\frac{2\pi}{T}=\frac{2\pi}{2}=\pi.$ Hence $y=A\sin(\omega x)=3\sin(\pi x).$
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