u[a_,b_]:={Cos[a]Cos[b],Cos[a]Sin[b],Sin[a]};

sin12[a1_,a2_,b1_,b2_]:= Norm[Cross[u[a1,b1],u[a2,b2]]]

sin12[0,0,x,y]

FullSimplify[%]

sint = sin12[40 Degree,45 Degree,145  Degree,164 Degree]

N[ArcSin[sint]/Degree]

Func[t_]:=5 10^4 + 28 10^4((2 BesselJ[1,2 Pi 1.5/0.21 Sin[14.8 Degree (t-1250)/3600.]])/(2 Pi 1.5/0.21 Sin[14.8 Degree (t-1250)/3600]))^2

Plot[Func[t],{t,0,3500},PlotRange->{All,All},AspectRatio->1.2,PlotStyle->{Red,Thick,Dashed}]