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: 40

Answer

Refer to the graph below.
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Work Step by Step

RECALL: The graph of the function $y=c+a\cdot \sin{(bx)}$ is a sinusoidal curve that has: period = $\frac{2\pi}{b}$ amplitude = $|a|$ one period is in the interval $[0, \frac{2\pi}{b}]$ vertical shift = $|c|$ (upward when $c\gt0$ and downward when $c\lt0$) The given function has $a=-3, b=2,$ and $c=-1$. Thus, the graph of this function has: period = $\frac{2\pi}{2}=\pi$ amplitude = $|-3| = 3$ vertical shift = $|-1|=1$, downward Since $a$ is negative, the graph also involves a reflection about the x-axis of the parent function. One period of this function will be in the interval $[0, \pi]$. Divide this interval into four equal parts to get the key x-values $0, \frac{\pi}{4}, \frac{\pi}{2}, \frac{3\pi}{4}, \pi$. 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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