Precalculus: Mathematics for Calculus, 7th Edition

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

Chapter 5 - Review - Exercises - Page 463: 32

Answer

Amplitude is 2 period is 2$\pi$ Horizontal shift is $\frac{\pi}{4}$

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 $sin$(1(x-\frac{\pi}{4}))$ 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 $\frac{2\pi}{1}=2\pi$. And the horizontal shift is represented by $b$, which, in this case, is $\frac{\pi}{4}$.
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