In trigonometry,
[tex]\csc x\text{ =}\frac{1}{\sin x}[/tex]
So we can rewrite the question as
[tex]y=\frac{1}{\sin x}[/tex][tex]\begin{gathered} At\text{ x= 0,}\pi,2\pi \\ y=\frac{1}{\sin 0}=\infty\text{ (infinity or discontinuity)} \end{gathered}[/tex][tex]y=\frac{1}{\sin \text{ }\pi}=\text{ }\infty[/tex]
The same results apply to
[tex]2\pi[/tex]
At
[tex]\begin{gathered} x=\frac{\pi}{2}\text{ and x=}\frac{3\pi}{2} \\ y=1\text{ and -1} \end{gathered}[/tex]
So from the above result, the best(correct) option that represents
[tex]y=\csc x[/tex]
Is option D
Graph D is the right answer.
