Precalculus: Mathematics for Calculus, 7th Edition

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

Chapter 5 - Review - Test - Page 465: 7

Answer

Amplitude: 2 Period: $4\pi$ Phase $1/2$ Horizontal shift: $\pi/3$

Work Step by Step

First, one must convert the equation to the following form $y=a\cdot $sin$(k(x-b))$, so it will be $y=2\cdot $sin$(\frac{1}{2}(x-\frac{\pi}{3}))$ Now one can find the data. The amplitude is $|a|$ which is $2$ in this example. The period is found using $\frac{2\pi}{k}$, so $\frac{2\pi}{1/2}=4\pi$. The phase is $k$, which is $1/2$. And the horizontal shift is represented by $b$, which, in this case, is $\pi/3$.
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