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: 32

Answer

Refer to the graph below.
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Work Step by Step

RECALL: The function $y=\tan{(bx)}$ has a period of $\frac{\pi}{|b|}$. The given function has $b=3$. Thus, it has: period = $\frac{\pi}{3}$ The consecutive vertical asymptotes of this function are $x=-\frac{\pi}{12}$ and $\frac{\pi}{12}$. One period of this function is in the interval $[-\frac{\pi}{6}, \frac{\pi}{6}]$. Divide this interval into four equal parts to obtain the key x-values $-\frac{\pi}{12}, 0, \frac{\pi}{12}$. 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) Graph the consecutive vertical asymptotes mentioned above. (3) 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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