$Assumptions={n,m}∈Integers&&{n,m}>=1&&0<=Sin[n t];

PowerExpand@FullSimplify@Reduce[Sin[n t]==Sin[m t],{n,m}]

f[n_,t_]:=ConditionalExpression[Pi^(-1/2)Sin[n t],0<=t<=Pi &&n∈Integers&&n>=1];

Plot[Table[f[n,t],{n,3}],{t,0,Pi}]