## 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 162: 49

#### Answer

Refer to the graph below. #### Work Step by Step

The parent function of $y=-3+2\sin{x}$ is $y=\sin{x}$. The parent function $y=\sin{x}$ has a period of $2\pi$ so one period of its graph is in the interval $[0, 2\pi]$. Dividing this interval into four equal parts yield the key x-values $0, \frac{\pi}{2}, \pi, \frac{3\pi}{2}$ and $2\pi$. To graph the given function, perform the following steps: (1) Create a table of values for $y=-3+2\sin{x}$ using the key x-values listed above. (Refer to the table below.) (2) Plot each point from the table of values and connect them using a sinusoidal curve to complete one period in the interval $[0, 2\pi]$. (3) Extend the graph one more period by repeating the cycle in the interval $[2\pi, 4\pi]$. Refer to the graph in the answer part above. 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.