Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 5 - Trigonometric Functions - Section 5.4 Graphs of the Sine and Cosine Functions* - 5.4 Assess Your Understanding - Page 431: 18


Amplitude=$\dfrac{4}{3}$ Period= $3\pi$

Work Step by Step

Recall: For $y=A\sin{(ωx)}$, we have: $\text{Amplitude}=|A|\quad \quad \text{and} \quad \quad \text{Period}=T=\frac{2\pi}{ω}$ In $y=\frac{4}{3}\sin (\frac{2}{3}x)$we have $A=\frac{4}{3}$ and $\omega=\frac{2}{3}$, so Amplitude= $|A|=|\frac{4}{3}|=\frac{4}{3}$ Period $T=\frac{2\pi}{\omega}=\dfrac{2\pi}{\frac{2}{3}}=3\pi$
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