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: 32

Answer

$\text{(D)}$

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, $y=-2\sin(\frac{1}{2}x)$ Amplitude=$|-2|=2$ Period: $T=\frac{2\pi}{\frac{1}{2}}=4\pi$ Also, the sine function has a y-intercept at the origin, $y=0$. When $x=\pi$, the value of the function is: $y=-2\sin{(\frac{\pi}{2})}=-2(1)=-2$ The graph that has the same characteristics is $\text{(D)}$.
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