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 162: 39

Answer

Refer to the blue graph below.
1523851307

Work Step by Step

RECALL: The graph of $y=\sin{(x-d)}$ involves a horizontal shift of the parent function $y=\sin{x}$. The shift is $d$ units to the right when $d \gt 0$ and $|d|$ units to the left when $d\lt0$. The given function has $d=-\frac{\pi}{4}$, which is negaitive. Thus, the given function involves a $\frac{\pi}{4}$-unit shift to the left of the parent function $y=\sin{x}$. To graph the given function, perform the following steps: (1) Graph the parent function $y=\sin{x}$ over a two-period interval, which is $[0, 4\pi]$. (Refer to the red graph in the answer part above.) (2) Shift the graph of the parent function $\frac{\pi}{4}$ units to the left. (Refer to the blue graph in the answer part above.)
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.