Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 4 - Section 4.3 - Vertical and Horizontal Translations - 4.3 Problem Set - Page 217: 20

Answer

$Amplitude = \frac{1}{2}$ $Period = \frac{2\pi}{3}$ $Vertical\ translation = 1\ units\ upward$ See below

Work Step by Step

We know that If C is any real number and $B> 0$, then the graphs of $y = k + A\sin(Bx+C)$ and $y = k + A\cos (Bx+C)$ will have $Amplitude = |A|$ $Period = \frac{2\pi}{B}$ $ Vertical\ translation = k$ so for $y = 1 + \frac{1}{2} \sin 3x$ $Amplitude = |\frac{1}{2}| = \frac{1}{2}$ $Period = \frac{2\pi}{3}$ $ Vertical\ translation = 1 = 1\ units\ upward$
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