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: 8



Work Step by Step

The function is $y=-\cot x$. In the general equation $y=a\cot bx$, when $a\lt0$, the graph is reflected across the x-axis. In addition, comparing $y=-\cot x$ to $y=a\cot bx$, we find that $b=1$. The value of $b$ can be used to find the location of the two vertical asymptotes: $bx=0$ and $bx=\pi$ $1x=0$ and $1x=\pi$ $x=0$ and $x=\pi$ Therefore, the location of the asymptotes is the same as that of the graph of $\cot x$. Therefore, using this information, we can ascertain that the graph of $y=-\cot x$ will be the same as the graph of $y=\cot x$ except that it will be reflected across the x-axis. This means that the correct graph for $y=-\cot x$ is A.
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