Chapter 4 - Graphs of the Circular Functions - Section 4.4 Graphs of the Secant and Cosecant Functions - 4.4 Exercises - Page 179: 7

$B$

The cosecant function is undefined when $x=..., -3\pi, -2\pi, -\pi, 0,\pi,2\pi, 3\pi...$ Thus, its graph has the vertical asymptotes $x=..., -3\pi, -2\pi, -\pi, 0, \pi, 2\pi, 3\pi, ...$ This means that the possible graphs of $y=−\csc{x}$ are the ones in Options B and D. Note that when $x=\frac{\pi}{2}$ , the value of $y=−\csc{x}$ is $-1$. Only the graph in Option B satisfies this. Thus, the graph of $y=−\csc{x}$ must be the one in Option B.