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 - Section 4.2 Translations of the Graphs of the Sine and Cosine Functions - 4.2 Exercises - Page 162: 60


Refer to the graph below.

Work Step by Step

The given equation is already in the form $y=c+a\cdot \cos{[b(x-d)]}$. Find one interval of the given function whose length is one period: \begin{array}{ccccc} &0 &\le &3\left(x-\frac{\pi}{6}\right)&\le &2\pi \\&\frac{0}{3}&\le &\frac{3\left(x-\frac{\pi}{6}\right)}{3} &\le &\frac{2\pi}{3} \\&0 &\le &x-\frac{\pi}{6} &\le &\frac{2\pi}{3} \\&0+\frac{\pi}{6} &\le &x-\frac{\pi}{6}+\frac{\pi}{6} &\le &\frac{2\pi}{3}+\frac{\pi}{6} \\&\frac{\pi}{6} &\le &x &\le &\frac{5\pi}{6} \end{array} Thus, one interval of the given function is $[\frac{\pi}{6}, \frac{5\pi}{6}]$. Dividing this interval into four equal parts yield the key x-values $\frac{\pi}{6}, \frac{\pi}{3}, \frac{\pi}{2}, \frac{2\pi}{3}, $ and $\frac{5\pi}{6}$. To graph the given function, perform the following steps: (1) Create a table of values for the function $y=-\frac{5}{2}+\cos{\left(3(x-\frac{\pi}{6})\right)}$ using the key x-values listed above. (Refer to the table below.) (2) Plot each point in the table then connect them using a sinusoidal curve. (Refer to the attached graph in the answer part above.)
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