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: 27


See graph and explanations.

Work Step by Step

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