Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 4 - Review Exercises - Page 190: 39

Answer

Refer to the graph below.
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Work Step by Step

RECALL: The graph of the function $y=a\cdot \cos{[b(x-d)]}+c$ is a sinusoidal curve that has: period = $\frac{2\pi}{b}$ amplitude = $|a|$ phase shift = $|d|$ (to the left when $d\lt0$, to the right when $d\gt0$) one period is in the interval $[0, 2\pi]$ vertical shift = $|c|$ (upward when $|c|\gt0$, downward when $c\lt0$) The given function has $a=2, b=3,c=1$ and $d=0$ Thus, the graph of this function has: period = $\frac{2\pi}{3}$ amplitude = $|2| = 2$ phase shift = 0 (none) vertical shift = $|1|=1$, upward One period of this function will be in the interval $[0, \frac{2\pi}{3}]$. Divide this interval into four equal parts to get the key x-values $0, \frac{\pi}{6}, \frac{\pi}{3}, \frac{\pi}{2}, \frac{2\pi}{3}$. To graph the given function, perform the following steps: (1) Create a table of values using the key x-values listed above. (Refer to the table below.) (2) Plot the points from the table of values and connect them using a sinusoidal curve. (Refer to the graph in the answer part above.)
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