Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 5 - Section 5.3 - Trigonometric Graphs - 5.3 Exercises - Page 429: 13

Answer

please see image

Work Step by Step

1. Start with the parent function $f(x)=\sin x$ (Graph:red dashed , amplitude 1, period $ 2\pi$) If plotting by hand, use Table 2 on page 420 to plot 13 points on $[0,2\pi]$, 2. The graph of $-\displaystyle \frac{1}{2}\sin x=-\frac{1}{2}f(x)$ is obtained from f(x) by reflecting f(x) about the x-axis $y=-f(x)$ , (green), then vertically compressing that graph by factor $\displaystyle \frac{1}{2}$. The new amplitude is $\displaystyle \frac{1}{2}$. Period remains same. Graphing utility used: online calculator desmos.com. The "wrench" button is used to set viewing window settings: radians, step $\pi/2$, ... (see image below) The accompanying table gives a sufficient number of points for graphing by hand. .
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