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: 42


Refer to the blue graph below.

Work Step by Step

RECALL: The graph of $y=a \cdot \sin{(x-d)}$ has an amplitude of $|a|$ units and 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 $a=3$ and $d=\frac{3\pi}{2}$, which is positive. Thus, the given function has an amplitude of $3$ and involves a $\frac{3\pi}{2}$-unit shift to the right of the function $y=a \cdot \sin{x}$. To graph the given function, perform the following steps: (1) Graph the function $y= 3 \sin{x}$ 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 function in (1) above $\frac{3\pi}{2}$ units to the right. (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.