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


Refer to the blue graph below.

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.)
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