Tangent vector - visualization of the definition

(Subscript[t, 0])=0.2;
f[t_]={Sin[2t],Cos[t]};
Manipulate[
plot1=ParametricPlot[f[t],{t,0,2}];
plot2=Graphics[Arrow[{f[(Subscript[t, 0])],f[(Subscript[t, 0])]+f'[(Subscript[t, 0])]}]]; (*Tangent vector f'((Subscript[t, 0]))*)
plot3=Graphics[Arrow[{f[(Subscript[t, 0])],f[(Subscript[t, 0])]+((f'[(Subscript[t, 0])])/(Sqrt[f'[(Subscript[t, 0])][[1]]^2+f'[(Subscript[t, 0])][[2]]^2]))}]]; (*Unit tangent vector T=f'((Subscript[t, 0]))/||f'((Subscript[t, 0]))||*)
plot4=Graphics[Style[Arrow[{f[(Subscript[t, 0])],f[(Subscript[t, 0])]+((f[(Subscript[t, 0])+h]-f[(Subscript[t, 0])])/h)}],Red]]; (*Secant vector, equal to the difference quotient*)
plot5=ListPlot[{f[(Subscript[t, 0])],f[(Subscript[t, 0])+h]},PlotMarkers->●];
plot6=Graphics[{Style[Arrow[{{0,0},f[(Subscript[t, 0])]}],Blue],Style[Arrow[{{0,0},f[(Subscript[t, 0])+h]}],Blue]}];(*Position vectors*)
labels=Graphics[{
Text[Style["\!\(\*
StyleBox[FractionBox[
RowBox[{
RowBox[{"f", 
RowBox[{"(", 
RowBox[{SubscriptBox["t", "0"], "+", "h"}], ")"}]}], "-", 
RowBox[{"f", 
RowBox[{"(", SubscriptBox["t", "0"], ")"}]}]}], "h"],
FontSize->14]\)",Red],f[(Subscript[t, 0])]+((f[(Subscript[t, 0])+h]-f[(Subscript[t, 0])])/h)+{-0.1,-0.2}],
Text["T",f[(Subscript[t, 0])]+((f'[(Subscript[t, 0])])/(Sqrt[f'[(Subscript[t, 0])][[1]]^2+f'[(Subscript[t, 0])][[2]]^2]))+{0,0.1}],

Text["f'((Subscript[t, 0]))",f[(Subscript[t, 0])]+f'[(Subscript[t, 0])]+{-0.1,0.1}],
Text[Style["f((Subscript[t, 0]))",Blue],f[(Subscript[t, 0])]+{-0.15,-0.1}],
Text[Style["f((Subscript[t, 0])+h)",Blue],f[(Subscript[t, 0])+h]+{-0.3,0}]
}];
Show[plot1,plot2,plot3,plot4,plot5,plot6,labels,PlotRange->All,Ticks->None],
{h,0.6,0.01,0.01}
]

Drawing a helix curve

f[t_]:={Cos[t],Sin[t],t}
Manipulate[
plot1=ParametricPlot3D[f[t],{t,0,T},AxesLabel->{"x","y","z"}];
plot2=Graphics3D[Arrow[{{0,0,0},f[T]}]];(*position vector*)
plot3=Graphics3D[Arrow[{f[T],f[T]+((f'[T])/(Sqrt[f'[T][[1]]^2+f'[T][[2]]^2]))}]];(*unit tangent vector*)
labels=Graphics3D[{
Text["f(t)",f[T]/2+{-0.5,-0.5,0}],
Text["T=((f' (t))/(||f' (t)||))",f[T]+((f'[T])/(Sqrt[f'[T][[1]]^2+f'[T][[2]]^2]))+{0.75 ,0.75,0}]}];
Show[plot1,plot2,plot3,labels,PlotRange->{{-3,3},{-3,3},{0,15}}],
{T,1,10}
]