Answered
I'm working on a trigonometric graphic calculator, and I'd like for the graphic view to NOT show the vertical asymptotes of the csc(x), sec(x), tan(x), and cot(x) functions.
Strangely, Geogebra only displays the vertical asymptotes of the tan(x) and sec(x) functions, but not the other two functions. Why is this?
The same question 
I do not see them in windows or https://www.geogebra.org/graphing or android
where do you see them?
I think the question is different:
"Strangely, Geogebra only displays the vertical asymptotes of the tan(x)
and sec(x) functions, but not the other two functions. Why is this?"
I tried that at the WebApp of GeoGebra and got for every function one asymptote in a List.
I assume you are referring to this worksheet:
https://www.geogebra.org/m/KzETDRAj
short aswer: try changing the visible area by moving or zooming the view.
long answer: You are seeing extra vertical lines because it's hard for GeoGebra (or other function plotting software) to determine where are the discontinuities. Let's assume one pixel represents 0.02 units. GeoGebra computes case f(x) and f(x+0.02), if they differ a lot it assumes there is discontinuity and does not connect the points, otherwise it draws a line between (x,f(x)) and (x+0.02,f(x+0.02)). Problem is what "differs a lot" means -- if the threshold is too low we would miss parts of continuous functions, if it's too high we get the extra vertical asymptotes.
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