Manipulate[
Plot[
a1 Sin[( x)]+a2 Sin[2( x)]+a3 Sin[3( x)]+a4 Sin[4( x)]+a5 Sin[5( x)]+a6 Sin[6( x)]+a7 Sin[7( x)]+a8 Sin[8( x)]+a9 Sin[9( x)]+a10 Sin[10( x)]+b0+b1 Cos[( x)]+b2 Cos[2( x)]+b3 Cos[3( x)]+b4 Cos[4( x)]+b5 Cos[5( x)]+b6 Cos[6( x)]+b7 Cos[7( x)]+b8 Cos[8( x)]+b9 Cos[9( x)]+b10 Cos[10( x)],{x,-10,10},
PlotRange->{{-10,10},{-5,5}},
PlotStyle->{{Blue}},
Ticks->{{-3π,-2π,-π,π,2π,3π},{ -4,-3,-2,-1,1,2,3,4}},
AxesLabel->{"x","f(x)"},
LabelStyle->({FontSize->16,FontFamily->"Times"}),
ImageSize->{400,300}
],
(* setup the controls *)
Style["harmonics",Bold],
Delimiter,
Style["sine terms",Bold],
{{a1,0,"(Subscript[a, 1])"},-1,1,Appearance->"Labeled",ImageSize->Tiny},
{{a2,0,"(Subscript[a, 2])"},-1,1,Appearance->"Labeled",ImageSize->Tiny},
{{a3,0,"(Subscript[a, 3])"},-1,1,Appearance->"Labeled",ImageSize->Tiny},
{{a4,0,"(Subscript[a, 4])"},-1,1,Appearance->"Labeled",ImageSize->Tiny},
{{a5,0,"(Subscript[a, 5])"},-1,1,Appearance->"Labeled",ImageSize->Tiny},
{{a6,0,"(Subscript[a, 6])"},-1,1,Appearance->"Labeled",ImageSize->Tiny},
{{a7,0,"(Subscript[a, 7])"},-1,1,Appearance->"Labeled",ImageSize->Tiny},
{{a8,0,"(Subscript[a, 8])"},-1,1,Appearance->"Labeled",ImageSize->Tiny},
{{a9,0,"(Subscript[a, 9])"},-1,1,Appearance->"Labeled",ImageSize->Tiny},
{{a10,0,"(Subscript[a, 10])"},-1,1,Appearance->"Labeled",ImageSize->Tiny},
Delimiter,
Style["cosine terms",Bold],
{{b0,0,"(Subscript[b, 0])"},-1,1,Appearance->"Labeled",ImageSize->Tiny},
{{b1,0,"(Subscript[b, 1])"},-1,1,Appearance->"Labeled",ImageSize->Tiny},
{{b2,0,"(Subscript[b, 2])"},-1,1,Appearance->"Labeled",ImageSize->Tiny},
{{b3,0,"(Subscript[b, 3])"},-1,1,Appearance->"Labeled",ImageSize->Tiny},
{{b4,0,"(Subscript[b, 4])"},-1,1,Appearance->"Labeled",ImageSize->Tiny},
{{b5,0,"(Subscript[b, 5])"},-1,1,Appearance->"Labeled",ImageSize->Tiny},
{{b6,0,"(Subscript[b, 6])"},-1,1,Appearance->"Labeled",ImageSize->Tiny},
{{b7,0,"(Subscript[b, 7])"},-1,1,Appearance->"Labeled",ImageSize->Tiny},
{{b8,0,"(Subscript[b, 8])"},-1,1,Appearance->"Labeled",ImageSize->Tiny},
{{b9,0,"(Subscript[b, 9])"},-1,1,Appearance->"Labeled",ImageSize->Tiny},
{{b10,0,"(Subscript[b, 10])"},-1,1,Appearance->"Labeled",ImageSize->Tiny},
AutorunSequencing->{1}
SaveDefinitions->True]