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: 20


Refer to the graph below.

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 $b=\frac{1}{2}$, the period of the given function is $\frac{\pi}{\frac{1}{2}}=2\pi$. Consecutive vertical asymptotes of the given function are $x=0$ and $2\pi$. This means that one period of the given function is in the interval $[0, 2\pi]$. Dividing this interval into four equal parts give the key x-values: $\frac{\pi}{2}, \pi, \frac{3\pi}{2}$. 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.
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