Print["T0(x)="ChebyshevT[0,x]];
Print["T1(x)="ChebyshevT[1,x]]
Print["T2(x)="ChebyshevT[2,x]];
Print["T3(x)="ChebyshevT[3,x]]
Print["T4(x)="ChebyshevT[4,x]];
Print["T5(x)="ChebyshevT[5,x]]

Print["       The function is T5[x] "];
T5zero = Table[{N[Cos[(2i+1) Pi / 10]], 0}, {i, 0, 4}];
T5dots = ListPlot[T5zero,PlotStyle->{PointSize[0.02]},
                DisplayFunction->Identity];
T5=Plot[ChebyshevT[5,x], {x,-1,1},
DisplayFunction->Identity];
Show[T5,T5dots,DisplayFunction->$DisplayFunction]

Print["       The function is T10[x] "];
T10zero = Table[{N[Cos[(2i+1) Pi / 20]], 0}, {i, 0, 9}];
T10dots = ListPlot[T10zero,PlotStyle->{PointSize[0.02]},
                DisplayFunction->Identity];
T10=Plot[ChebyshevT[10,x], {x,-1,1},
DisplayFunction->Identity];
Show[T10,T10dots,DisplayFunction->$DisplayFunction]

Clear[f];
f[x_] = 1 /(1+ 25x^2)

Plot[f[x], {x, -1, 1}]

Clear[data];
data= Table[{Cos[(2i+1) Pi /20]//N, 
f[Cos[(2i+1) Pi /20]//N]},{i, 0, 9}] ;

g[x_]= InterpolatingPolynomial[data, x];
Q[x] = Expand[g[x]]

dots = ListPlot[data,PlotStyle->{PointSize[0.02]},
                DisplayFunction->Identity];
g1=Plot[{f[x], g[x]}, {x, -1,1},
DisplayFunction->Identity];
Show[g1,dots,PlotRange->{{-1,1},{0,1}},
PlotLabel->"f(x) and the interpolating polynomial.",
AxesLabel->{"x","y"},DisplayFunction->$DisplayFunction];