y1[x_]:=Sin[x];{x1,x2}={-Pi/2,Pi/2};
y1i[x_]:=ArcSin[x];{x1i,x2i}={-1,1};
axeslabel={x,y};
plotlabel={ToString[y1[x]],ToSting[y1i[x]]};
ploty1=Plot[y1[x],{x,x1,x2},PlotLabel->plotlabel,AxesLabel->axeslabel];
ploty1i=Plot[y1i[x],{x,x1i,x2i},PlotLabel->plotlabel,AxesLabel->axeslabel,PlotStyle->{Thick,Dotted}];
xl=Min[{x1,x1i}];xr=Max[{x2,x2i}];
ylinear[x_]:=x;
plotylinear=Plot[ylinear[x],{x,xl,xr},PlotLabel->plotlabel,AxesLabel->axeslabel,PlotStyle->{Red,Dotted}];
plotlabel={ToString[y1[x]],ToString[y1i[x]]};
Plot[{y1[x],y1i[x],ylinear[x]},{x,xl,xr},PlotLabel->plotlabel,AxesLabel->axeslabel,AspectRatio->1];

Show[{plotylinear,ploty1i,ploty1}]

y1[x_]:=Cos[x];{x1,x2}={0,Pi};
y1i[x_]:=ArcCos[x];{x1i,x2i}={-1,1};
axeslabel={x,y};
plotlabel={ToString[y1[x]],ToSting[y1i[x]]};
ploty1=Plot[y1[x],{x,x1,x2},PlotLabel->plotlabel,AxesLabel->axeslabel];
ploty1i=Plot[y1i[x],{x,x1i,x2i},PlotLabel->plotlabel,AxesLabel->axeslabel,PlotStyle->{Thick,Dotted}];
xl=Min[{x1,x1i}];xr=Max[{x2,x2i}];
ylinear[x_]:=x;
plotylinear=Plot[ylinear[x],{x,xl,xr},PlotLabel->plotlabel,AxesLabel->axeslabel,PlotStyle->{Red,Dotted}];
plotlabel={ToString[y1[x]],ToString[y1i[x]]};
Plot[{y1[x],y1i[x],ylinear[x]},{x,xl,xr},PlotLabel->plotlabel,AxesLabel->axeslabel,AspectRatio->1];

Show[{plotylinear,ploty1i,ploty1}]

y1[x_]:=Tan[x];{x1,x2}={-Pi/2,Pi/2};
y1i[x_]:=ArcTan[x];{x1i,x2i}={-10,10};
axeslabel={x,y};
plotlabel={ToString[y1[x]],ToSting[y1i[x]]};
ploty1=Plot[y1[x],{x,x1,x2},PlotLabel->plotlabel,AxesLabel->axeslabel];
ploty1i=Plot[y1i[x],{x,x1i,x2i},PlotLabel->plotlabel,AxesLabel->axeslabel,PlotStyle->{Thick,Dotted}];
xl=Min[{x1,x1i}];xr=Max[{x2,x2i}];
ylinear[x_]:=x;
plotylinear=Plot[ylinear[x],{x,xl,xr},PlotLabel->plotlabel,AxesLabel->axeslabel,PlotStyle->{Red,Dotted}];
plotlabel={ToString[y1[x]],ToString[y1i[x]]};
Plot[{y1[x],y1i[x],ylinear[x]},{x,xl,xr},PlotLabel->plotlabel,AxesLabel->axeslabel,AspectRatio->1];

Show[{plotylinear,ploty1i,ploty1}]

y1[x_]:=Csc[x];{x1,x2}={-Pi/2,Pi/2};
y1i[x_]:=ArcCsc[x];{x1i,x2i}={-10,10};
axeslabel={x,y};
plotlabel={ToString[y1[x]],ToSting[y1i[x]]};
ploty1=Plot[y1[x],{x,x1,x2},PlotLabel->plotlabel,AxesLabel->axeslabel];
ploty1i=Plot[y1i[x],{x,x1i,x2i},PlotLabel->plotlabel,AxesLabel->axeslabel,PlotStyle->{Thick,Dotted}];
xl=Min[{x1,x1i}];xr=Max[{x2,x2i}];
ylinear[x_]:=x;
plotylinear=Plot[ylinear[x],{x,xl,xr},PlotLabel->plotlabel,AxesLabel->axeslabel,PlotStyle->{Red,Dotted}];
plotlabel={ToString[y1[x]],ToString[y1i[x]]};
Plot[{y1[x],y1i[x],ylinear[x]},{x,xl,xr},PlotLabel->plotlabel,AxesLabel->axeslabel,AspectRatio->1];

Show[{plotylinear,ploty1i,ploty1}]

y1[x_]:=Sec[x];{x1,x2}={0,Pi/2};
y1i[x_]:=ArcSec[x];{x1i,x2i}={-10,10};
axeslabel={x,y};
plotlabel={ToString[y1[x]],ToSting[y1i[x]]};
ploty1=Plot[y1[x],{x,x1,x2},PlotLabel->plotlabel,AxesLabel->axeslabel];
ploty1i=Plot[y1i[x],{x,x1i,x2i},PlotLabel->plotlabel,AxesLabel->axeslabel,PlotStyle->{Thick,Dotted}];
xl=Min[{x1,x1i}];xr=Max[{x2,x2i}];
ylinear[x_]:=x;
plotylinear=Plot[ylinear[x],{x,0,xr},PlotLabel->plotlabel,AxesLabel->axeslabel,PlotStyle->{Red,Dotted}];
plotlabel={ToString[y1[x]],ToString[y1i[x]]};
Plot[{y1[x],y1i[x],ylinear[x]},{x,xl,xr},PlotLabel->plotlabel,AxesLabel->axeslabel,AspectRatio->1];

Show[{plotylinear,ploty1i,ploty1}]

y1[x_]:=Cot[x];{x1,x2}={0,Pi/2};
y1i[x_]:=ArcCot[x];{x1i,x2i}={-10,10};
axeslabel={x,y};
plotlabel={ToString[y1[x]],ToSting[y1i[x]]};
ploty1=Plot[y1[x],{x,x1,x2},PlotLabel->plotlabel,AxesLabel->axeslabel];
ploty1i=Plot[y1i[x],{x,x1i,x2i},PlotLabel->plotlabel,AxesLabel->axeslabel,PlotStyle->{Thick,Dotted}];
xl=Min[{x1,x1i}];xr=Max[{x2,x2i}];
ylinear[x_]:=x;
plotylinear=Plot[ylinear[x],{x,0,xr},PlotLabel->plotlabel,AxesLabel->axeslabel,PlotStyle->{Red,Dotted}];
plotlabel={ToString[y1[x]],ToString[y1i[x]]};
Plot[{y1[x],y1i[x],ylinear[x]},{x,xl,xr},PlotLabel->plotlabel,AxesLabel->axeslabel,AspectRatio->1];

Show[{plotylinear,ploty1i,ploty1}]