## Trigonometry (11th Edition) Clone

Published by Pearson

# Chapter 4 - Graphs of the Circular Functions - Section 4.2 Translations of the Graphs of the Sine and Cosine Functions - 4.2 Exercises - Page 160: 9

D

#### Work Step by Step

According to the text, the graph of the function $y=f(x-d)$ is translated horizontally compared to the graph of $y=f(x)$. If $d$ is greater than zero, the translation is $d$ units to the right and if $d$ is less than zero, the translation is $|d|$ units to the left. We now compare the equation $y=\sin(x-\frac{\pi}{4})$ to $y=f(x-d)$. Upon inspection, we find that $d=\frac{\pi}{4}$. Since $d$ is positive, the graph of $y=\sin(x-\frac{\pi}{4})$ will be the same as the graph of $y=\sin x$ except that it will be translated $\frac{\pi}{4}$ units to the right. Therefore, we need to find a graph which is the same as the graph of $y=\sin x$ except that it is translated $\frac{\pi}{4}$ units to the right. Such a graph is found in option D.

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