Manipulate[iMax = (n-1)/2;
Plot[{Sin[x],(∑_(i=0)^iMax)(((-1))^i)((x^(2i+1))/((2i+1)!))}, {x, -2Pi,2Pi}, PlotStyle -> Thickness[.005],PlotRange ->{-2, 2}, AxesLabel ->{x,y}, PlotLabel-> "y = Sin[x] and the Taylor Polynomial y = (Subscript[T, n])(x)"], {{n,1}, Range[0,17,1]}, ControlType -> Setter]

Manipulate[iMax = (n-1)/2;Plot[ Sin[x]-(∑_(i=0)^iMax)(((-1))^i)((x^(2i+1))/((2i+1)!)),{x, -2Pi, 2Pi},PlotStyle -> Thickness[.005], PlotRange ->{-2, 2}, AxesLabel ->{x,y}, PlotLabel -> "Error of Taylor Polynomial: y = sin(x) - (Subscript[T, n])(x)"], {n, Range[0,17,1]}, ControlType -> Setter]