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: 35

Answer

Refer to the graph below.
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Work Step by Step

RECALL: The function $y=a \cdot \cos{[b(x-d)]}$ (1) has a period of $\dfrac{2\pi}{|b|}$; (2) has an amplitude of $|a|$; and (3) involves a phase shift of $|d|$ of the parent function $y=\cos{x}$ (to the left when $d\lt0$, to the right when $d\gt0$) The given function has $a=1, b=1,$ and $d=\frac{\pi}{4}$. Thus, the given function has: period = $\frac{2\pi}{1}=2\pi$ amplitude = $|1|=1$ phase shift = $\frac{\pi}{4}$ to the right One period of the parent function $y=\cos{x}$ is in the interval $[0, 2\pi]$ The given function has a phase shift of $\frac{\pi}{4}$ to the right therefore one period would be in the interval $[\frac{\pi}{4}, \frac{9\pi}{4}]$. Divide this interval into four equal parts to obtain the key x-values $\frac{\pi}{4}, \frac{3\pi}{4} \frac{5\pi}{2}\frac{7\pi}{4}, \frac{9\pi}{4}$. 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 each point from the table of values then connect them using a sinusoidal curve. (Refer to the graph in the answer part above.)
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