Trig Bezier

We compare the effect of replacing (1 - t), t by Cos^2[t], Sin^2[t]

bernex[n_,i_,t_]:=Binomial[n,i]*(1-t)^(n-i)*t^i;
berntrig[n_,i_,t_]:=Binomial[n,i]*(Cos[t])^(2(n-i))*Sin[t]^(2i);

b={{0,0},{2,0},{3,0.8},{3,1.5}};
n=Length[b]-1;

curvex=ParametricPlot[Sum[bernex[n,i,t]*b[[i+1]],{i,0,n}],{t,0,3.0},PlotStyle->{Thick, Green}];
curvetrig=ParametricPlot[Sum[berntrig[n,i,t]*b[[i+1]],{i,0,n}],{t,0,Pi/2},PlotStyle->{Thick, Red,Dashed}];
poly=Graphics[{Thick,Line[b]}];
points=Graphics[{PointSize[Large],Point[b]}];
pointrig[t_]:=Graphics[{PointSize[Large],Red,Point[Sum[berntrig[n,i,t]*b[[i+1]],{i,0,n}]]}];
pointex[t_]:=Graphics[{PointSize[Large],Green,Point[Sum[bernex[n,i,t]*b[[i+1]],{i,0,n}]]}];
Manipulate[
Show[{poly,points,curvex,curvetrig,pointex[t](*pointrig[t]*)}],{t,0.001,3.0}]