## Trigonometry (11th Edition) Clone

Published by Pearson

# Chapter 4 - Graphs of the Circular Functions - Section 4.1 Graphs of the Sine and Cosine Functions - 4.1 Exercises - Page 149: 38

#### Answer

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

RECALL: The functions $y=a \cdot \sin{bx}$ and $y=a \cdot \cos{bx}$ have: period = $\dfrac{2\pi}{b}$ amplitude = $|a|$ The given function has $a=-\frac{2}{3}$ and $b=\frac{\pi}{4}$ thus period = $\dfrac{2\pi}{\frac{\pi}{4}}=8$ amplitude = $|-\frac{2}{3}| = \frac{2}{3}$ To graph the function, perform the following steps: (1) With a period of $8$, one period of the function is over the interval $[0, 8]$. (2) Divide this interval into four parts to obtain the x-values $0, 2, 4, 6, \text{ and } 8$. (3) Make a table of values using the x-values above. (Refer to the table below.) (4) Plot the five points of the table of values then connect them using a sinusoidal curve whose amplitude is $\frac{2}{3}$. (5) Repeat the cycle of the graph form one more period, which is $[8, 16]$. (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.