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: 25


$y=-1+\sin x$

Work Step by Step

The graph is that of $y=\sin x$ except that it has been translated one unit down. Therefore, the graph is of the form $y=c+\sin x$. According to the rules of translating graphs, the translation is $c$ units up if $c$ is greater than zero. Conversely, the translation is $|c|$ units down if $c$ is less than zero. Since the graph is that of $y=\sin x$ which has been translated one unit down, the equation of the graph is $y=-1+\sin x$.
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