How to find the asymptotes of k(x) = 0.5csc(2x)?

Answer 1

since csc Ø = 1/sinØ
csc (2x) has asymptotes when sin(2x) = 0
(the amplitude won't matter)

sin(2x = 0
then
2x = 0 , ±π, ±2π , ±3π ....
x = 0 , ±π/2, ±π, ±3π/2 ...

http://www.wolframalpha.com/input/?i=plot+y+%3D+0.5csc%282x%29

the vertical lines are the asymptotes

Answer 2

So then could it be represented by pi(n)/2 ?

Answer 3

yes, you got it.

it would be x = nπ/2, where n is an integer.