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


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.)
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.