## 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: 13

B

#### Work Step by Step

According to the text, the graph of the function $y=c+f(x)$ is translated vertically compared to the graph of $y=f(x)$. If $c$ is greater than zero, the translation is $c$ units up and if $c$ is less than zero, the translation is $|c|$ units down. We now compare the equation $y=1+\sin x$ to $y=c+f(x)$. Upon inspection, we find that $c=1$. Since $c$ is positive, the graph of $y=1+\sin x$ will be the same as the graph of $y=\sin x$ except that it will be translated $1$ unit up. Therefore, we need to find a graph which is the same as the graph of $y=\sin x$ except that it is translated $1$ unit up. Such a graph is found in option B.

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