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 4.4 Graphs of the Secant and Cosecant Functions - 4.4 Exercises - Page 180: 27


$y=-2 + \csc{x}$

Work Step by Step

The graph has a period of $2\pi$ and looks similar to the graph of the basic cosecant function. Notice, however, that instead of having the vertices at $(\frac{\pi}{2}, 1)$ and $(\frac{3\pi}{2}, -1)$, the vertices of the ggiven graph are at $(\frac{\pi}{2}, -1)$ and $\frac{3\pi}{2}, -3)$. This means that the given graph involves a 2-unit downward shift of the parent function $y=\csc{x}$. Therefore, the equation of the function whose graph is given is $y=\csc{x} -2$ or $y=-2 + \csc{x}$.
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