## Trigonometry (11th Edition) Clone

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.)