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: 27



Work Step by Step

The amplitude and period can be calculated as, if $y=A\sin(wx)$: Amplitude=$|A|$ period: $T=\frac{2\pi}{w}$ In this function, $y=-3\sin(2x)$ Amplitude=$|-3|=3$ Period: $T=\frac{2\pi}{2}=\pi$ Also, the sine function has a $y$-intercept at the origin $y=0$. When $x=\frac{\pi}{4}$, the value of $y$ is $y=-3\sin{\frac{\pi}{4}}$, which is megative. The graph that has the same characteristics is $\text{(H)}$.
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