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 - Summary Exercises on Graphing Circular Functions - Page 181: 2


Refer to the graph below.

Work Step by Step

RECALL: The function $y=a \cdot \cos{(bx)}$ has: amplitude = $|a|$ period = $\frac{2\pi}{b}$ The given function has $a=4$ and $b=\frac{3}{2}$. Thus, the given function has: amplitude = $|4|=4$ period = $\frac{2\pi}{\frac{3}{2}}=\frac{4\pi}{3}$ This means that one period of the given function is in the interval $[0, \frac{4\pi}{3}]$. Divide this interval into four equal parts to obtain the key x-values $0, \frac{\pi}{3}, \frac{2\pi}{3}, \pi, \text{ and } \frac{4\pi}{3}$. To graph the given function, perform the following steps: (1) Create a table of values substituting each of the key x-values listed above into the given function. (Refer to the table below.) (2) Plot each point from the table then connect them using a sinusoidal curve.whose amplitude is $4$.
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