Precalculus (6th Edition) Blitzer

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

Chapter 4 - Section 4.6 - Graphs of Other Trigonometric Functions - Exercise Set - Page 610: 26

Answer

See graph and explanations.

Work Step by Step

Step 1. As $csc(4x)=\frac{1}{sin(4x)}$, we can use the original function $y=3sin(4x)$ to obtain the reciprocal function $y=3csc(4x)$. Step 2. The original function has zeros at $x=0,\pm \frac{\pi}{4}, \pm \frac{\pi}{2}, ...$ which become vertical asymptotes of the new function. Step 3. Using the reciprocal property, we can obtain the new function $y=3csc(4x)$ shown as the red curves in the figure.
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