## Trigonometry (11th Edition) Clone

Published by Pearson

# Chapter 4 - Graphs of the Circular Functions - Section 4.3 Graphs of the Tangent and Cotangent Functions - 4.3 Exercises - Page 171: 15

#### Answer

Refer to the graph below. #### Work Step by Step

RECALL: (1) The function $y=\tan{(bx)}$ is $\frac{\pi}{b}$. (2) The consecutive vertical asymptotes of the function $y=\tan{x}$ are $x=-\frac{\pi}{2}$ and $x=\frac{\pi}{2}$. Thus, with $b=1$, the period of the given function is $\pi$. Consecutive vertical asymptotes of the given function are $x=-\frac{\pi}{2}$ and $\frac{\pi}{2}$. This means that one period of the given function is in the interval $[-\frac{\pi}{2}, \frac{\pi}{2}]$. Dividing this interval into four equal parts give the key x-values: $-\frac{\pi}{4}, 0, \frac{\pi}{4}$. 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 aymptotes. (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. 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.