Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 11 - Section 11.1 - Finding Limits Using Tables and Graphs - Exercise Set - Page 1142: 98

Answer

amplitude $ 2$, period $ \pi$, phase shift $\phi=\frac{\pi}{4}$

Work Step by Step

Step 1. Given $y=2sin(2x-\frac{\pi}{2})=2sin2(x-\frac{\pi}{4})$, we can identify the amplitude as $|A|=2$, period as $p=\frac{2\pi}{2}=\pi$, and phase shift as $\phi=\frac{\pi}{4}$ Step 2. We can graph the function using transformations. From $y=sin(x)$, shift the curve $\frac{\pi}{4}$ to the right, shrink horizontally by a factor of 2, and stretch vertically by a factor of 2. The final graph is shown in the figure.
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