f[x_,n_]:=(∑_(k=0)^n)(((((-1))^k)(x^(2k+1)))/((2k+1)!))

Manipulate[
Show[GraphicsRow[{
Plot[{f[x,n],Sin[x]},{x,((-π)/2),(π/2)},PlotRange->{-2,2},PlotLabel->"sin(x)"],
Plot[{Abs[f[x,n]-Sin[x]]},{x,((-π)/2),(π/2)},PlotLabel->"error"]}]],

(*Manipulate Controllers*)
 Style["Actual Taylor Series Error",Bold,12],(*Title*)

{n,0,10,1},

(*Notes*)
Delimiter,
Style["",Plain,8],
Style["|error = (∑_(k = 0)^n)(((((-1))^k) (x^(2  k + 1)))/((2  k + 1)!)) - sin[x]|",Bold,8],
ControlPlacement->Left
]