Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 4 - Graphs of the Circular Functions - Section 4.2 Translations of the Graphs of the Sine and Cosine Functions - 4.2 Exercises - Page 161: 27


$y=\cos (x-\frac{\pi}{3})$

Work Step by Step

The graph is that of $y=\cos x$ except that it has been translated $\frac{\pi}{3}$ units to the right. Cosine graphs that are translated right or left are of the form $y=\cos (x-d)$. According to the rules of translating graphs, if the translation is $d$ units to the right, $d$ is greater than zero. Conversely, if the translation is $|d|$ units to the left, $d$ is less than zero. Therefore, as the graph has been translated $\frac{\pi}{3}$ units to the right, $d=\frac{\pi}{3}$. Therefore, its equation is $y=\cos (x-\frac{\pi}{3})$.
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