Question

pre cacl pleaseeeee help. the options are in the attachments as well

Answer 1

Answer:

The values of $x$ so that $y = \csc x$ have vertical asymptotes are $-2\pi$, $-\pi$, $0$, $\pi$, $2\pi$.

Step-by-step explanation:

The function cosecant is the reciprocal of the function sine and vertical asymptotes are located at values of $x$ so that function cosecant becomes undefined, that is, when function sine is zero, whose periodicity is $\pi$. Then, the  vertical asymptotes associated with function cosecant are located in the values of $x$ of the form:

$x = 0\pm \pi\cdot i$, $\forall \,i\in \mathbb{N}_{O}$

In other words, the values of $x$ so that $y = \csc x$ have vertical asymptotes are $-2\pi$, $-\pi$, $0$, $\pi$, $2\pi$.