Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 6 - Trigonometric Functions - 6.6 Phase Shift; Sinusoidal Curve Fitting - 6.6 Assess Your Understanding - Page 428: 21

Answer

See graph.

Work Step by Step

Step 1. Given $y=3csc(2x-\frac{\pi}{4})=3csc[2(x-\frac{\pi}{8})]$, we can find the period $p=\frac{2\pi}{2}=\pi$, and phase shift $\phi=\frac{\pi}{8}$. Step 2. To plot, start from one period of $y=csc(x)$, shift $\phi$ units to the right, shrink horizontally by a factor of $\frac{1}{2}$, then stretch vertically by a factor of $3$, and then use the period to repeat the resulting curve. See graph.
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