Question

Which function's graph has asymptotes located at the values x= ±nπ?

1-Y=csc x
2-Y=cos x
3-Y=tan x
4-Y=cot x

Answer 1

It's y = csc x and y = cot x.

Explanation:

Answer 2

`y=csc(\theta)`

`y=cot(\theta)`

Explanation:

I will just change

`x=\pm n\pi, n \in \mathbb{Z}_(\ge 0)`

For

`\theta = \pi n, n\in\mathbb{Z}`

Also, note that sine and cosine function don't have asymptotes.

The vertical asymptotes of cosecant occur every
`\pi n, n\in\mathbb{Z}`

It happens because the cosecant function is undefined for those values.

The cotangent function has asymptotes located at every integer multiple of
`\pi`.

On the other hand, the vertical asymptotes of tangent function occur at:

`$\theta=(\pi)/(2) +n \pi, n \in \mathbb{Z}$`

It happens because the tangent function is undefined for those values.