Manipulate[
Plot[Sin[x],{x,a,b}],
{{a,-2*π},-2*π,-π/2},{{b,2*π},π/2,2*π}]

Manipulate[Show[
Plot[ArcSin[x],{x,-1,1},ImageSize->Large,PlotRange->{{-π/2,π/2},{-π/2,π/2}},AspectRatio->1],
Plot[Sin[x],{x,-π/2,π/2},PlotStyle->{Opacity[S],Red}],
Plot[x,{x,-π/2,π/2},PlotStyle->{Opacity[D],Purple}]
],
{{S,0,"sin(x)"},{0,1}},{{D,0,"diagonal"},{0,1}}]

Manipulate[
Plot[Cos[x],{x,a,b}],
{{a,-2*π},-2*π,0},{{b,2*π},π,2*π}]

Manipulate[Show[
Plot[ArcCos[x],{x,-1,1},ImageSize->Large,PlotRange->{{-1,π},{-1,π}},AspectRatio->1],
Plot[Cos[x],{x,0,π},PlotStyle->{Opacity[S],Red}],
Plot[x,{x,-1,π},PlotStyle->{Opacity[D],Purple}]
],
{{S,0,"cos(x)"},{0,1}},{{D,0,"diagonal"},{0,1}}]

Manipulate[
Plot[Tan[x],{x,a,b}],
{{a,-2*π},-2*π,-π/2},{{b,2*π},π/2,2*π}]

Manipulate[Show[
Plot[ArcTan[x],{x,-5,5},ImageSize->Large,PlotRange->{{-5,5},{-5,5}},AspectRatio->1],
Plot[Tan[x],{x,-π/2,π/2},PlotStyle->{Opacity[S],Red}],
Plot[x,{x,-5,5},PlotStyle->{Opacity[D],Purple}]
],
{{S,0,"tan(x)"},{0,1}},{{D,0,"diagonal"},{0,1}}]