Chapter 4 - Graphs of the Circular Functions - Section 4.3 Graphs of the Tangent and Cotangent Functions - 4.3 Exercises - Page 171: 22 RECALL: (1) The period of the function $y=\tan{(bx)}$ is $\frac{\pi}{b}$. (2) The consecutive vertical asymptotes of the function $y=\tan{x}$, whose period is $\pi$, are $x=-\frac{\pi}{2}$ and $x=\frac{\pi}{2}$. Thus, with $b=\frac{1}{2}$, the period of the given function is $\frac{\pi}{\frac{1}{2}}=2\pi$. Consecutive vertical asymptotes of the given function are $x=-\pi$ and $\pi$. This means that one period of the given function is in the interval $[-\pi, \pi]$. Dividing this interval into four equal parts give the key x-values: $-\frac{\pi}{2}, 0, \frac{\pi}{2}$. To graph the given function, perform the following steps: (1) Create a table of values for the given function using the key x-values listed above. (Refer to the attached image table below.) (2) Graph the consecutive vertical asymptotes. (3) Plot each point from the table then connect them using a smooth curve, making sure that the curves are asymptotic with the lines in Step (2) above. Refer to the graph in the answer part above. 