Question

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

Answer 1

Answer:

$y=csc(\theta)$

$y=cot(\theta)$

Step-by-step 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:  

$\theta=\frac{\pi}{2} +n \pi, n \in \mathbb{Z}$

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