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: 11



Work Step by Step

The function is $y=\cot (x+\frac{\pi}{4})$. When we compare $y=\cot (x+\frac{\pi}{4})$ to the general form $y=c+a\cot (bx-d)$, we find that $d=-\frac{\pi}{4}$. $d$ represents the phase shift and since $d$ is negative, the phase shift is $\frac{\pi}{4}$ units to the left. Also, since $a=1$, $b=1$ and $c=0$, we can ascertain that the graph of $y=\cot (x+\frac{\pi}{4})$ will be the same as the graph of $y=\cot x$ except that it will be shifted $\frac{\pi}{4}$ units to the left. This means that the two vertical asymptotes will now be $0-\frac{\pi}{4}=-\frac{\pi}{4}$ and $\pi-\frac{\pi}{4}=\frac{3\pi}{4}$. This means that the correct graph for $y=\cot (x+\frac{\pi}{4})$ is F.
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