Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 0 - Before Calculus - 0.3 Families Of Function - Exercises Set 0.3 - Page 37: 28

Answer

True

Work Step by Step

To find the amplitude, we find the maximum of the function $y = -5sin(A \pi x)$. The maximum occurs when $sin(A \pi x)=-1$, causing $y = -5sin(A \pi x) = -5 * - 1 = 5$. Thus, the amplitude is 5. To find the period, we note that the period of the function $sin(Bx)$ is $\frac{2\pi}{|B|}$, where $B$ is the coefficient of the $x$ term in the sin function. In this case, the coefficient of the $x$ term in the sin function is $\pi A$. Thus, the period is $\frac{2\pi}{|\pi A|} = \frac{2}{|A|}$.
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