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: 34

Answer

Refer to the graph below.

Work Step by Step

RECALL: The function $y=a \cdot \cot{(bx)}$ has (1) a period of $\dfrac{\pi}{|b|}$; and (2) consecutive vertical asymptotes $x=0$ and $x=\frac{\pi}{|b|}$ The given function has $a=\frac{1}{2}$ and $b=3$. Thus, the given function has: period = $\frac{\pi}{3}$ One period of this function is in the interval $[0, \frac{\pi}{3}]$. Divide this interval into four equal parts to obtain the key x-values $0, \frac{\pi}{12}, \frac{\pi}{6}, \frac{\pi}{4}$. The consecutive vertical asymptotes of this function are $x=0$ and $x=\frac{\pi}{3}$. 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) Graph the consecutive vertical asymptotes listed above. (3) Plot each point from the table of values then connect them using a smooth curve. (Refer to the graph in the answer part above.)
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