Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 4 - Graphs of the Circular Functions - Section 4.3 Graphs of the Tangent and Cotangent Functions - 4.3 Exercises - Page 171: 23

Answer

Refer to the graph below.
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Work Step by Step

RECALL: (1) The period of the function $y=\cot{(bx)}$ is $\frac{\pi}{b}$. (2) The consecutive vertical asymptotes of the function $y=\cot{x}$, whose period is $\pi$, are $x=0$ and $x=\pi$. Thus, with $b=4$, the period of the given function is $\frac{\pi}{4}$. Consecutive vertical asymptotes of the given function are $x=0$ and $\frac{\pi}{4}$. This means that one period of the given function is in the interval $[0, \frac{\pi}{4}]$. Dividing this interval into four equal parts give the key x-values: $\frac{\pi}{16}, \frac{\pi}{8}, \frac{3\pi}{16}$. 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.
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