Question

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

Answer 1

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

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`.