Example.
Suppress the asymptotes from the graph of 
.
Show[SuppressAsymptotes[Plot[Csc[t],{t,0,4Pi}]]];
SuppressAsymptotes is an option to ODE. Setting SuppressAsymptotes->True attempts to suppress all vertical asymptotes associated with a two-dimensional graph. This option takes the form of a complex rule that replaces the Mathematica code for the graph with new Mathematica code for the graph in which the vertical asymptotes are eliminated. For example, if we assume that the Mathematica output is called plot, then the following code will apply the rule to plot.
SuppressAsymptotes[plot_]:=
plot //. {ax___,{a_,b_},{c_,d_},ay___} /;
Negative[Chop[b] Chop[d]] &&
Abs[(d-b)/(c-a)] > 2(MaxBend /. Options[Plot]) ->
{ax,Null,Null,ay}
Suppress the asymptotes from the graph of
Example.
.
Show[SuppressAsymptotes[Plot[Csc[t],{t,0,4Pi}]]];