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 408: 20


amplitude: $\frac{4}{3}$ period: $3\pi$

Work Step by Step

If a function has form $y=A\sin(\omega x)$, then there $|A|$ stands for the amplitude. First we identify $\omega$ and $A$ from the form of $y=A\sin{(\omega x)}$. Hence, $A=\left|\frac{4}{3}\right|=\frac{4}{3}$, $\omega=\frac{2}{3}.$ To get the period $T$ we can use the formula $T=\frac{2\pi}{\omega}$ to obtain $T=\dfrac{2\pi}{\frac{2}{3}}=3\pi$
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