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 38: 35

Answer

(a) Amplitude $= 3$, Period $= \frac{\pi}{2}$, refer to graph in picture (b) Amplitude $= 2$, Period $= 2$, refer to graph in picture (c) Amplitude $= 1$, Period $= 4 \pi$, refer to graph in picture

Work Step by Step

(a) $y = 3sin (4x)$ Amplitude($A$) $= 3$ Period($T$) $= \frac{1}{f}$ $2 \pi f = 4$ $f = \frac{4}{2 \pi} = \frac{2}{\pi}$ $T = \frac{1}{\frac{2}{\pi}} = \frac{\pi}{2}$ (b) $y = −2 cos πx$ Amplitude($A$) = $2$ $2 \pi f = \pi$ $f = \frac{\pi}{2 \pi} = \frac{1}{2}$ $T = \frac{1}{\frac{1}{2}} = 2$ (c) $y = 2 + cos (\frac{x}{2})$ Amplitude($A$) = $1$ $2 \pi f = \frac{1}{2}$ $f = \frac{\frac{1}{2}}{2 \pi} = \frac{1}{4\pi}$ $T = \frac{1}{\frac{1}{4 \pi}} = 4 \pi$
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