Funkcje cyklometryczne

Arcus sinus

Show[Plot[{Sin[x]},{x,-4,8},AspectRatio->Pi/15,ImageSize->800],
Plot[{Sin[x]},{x,-Pi/2,Pi/2},PlotStyle->Red],AxesLabel->{StyleForm["x",FontSize->20], StyleForm["sin(x)",FontSize->20]}]

Plot[{ArcSin[x]},{x,-1,1},ImageSize->400,PlotStyle->Red,AxesLabel->{StyleForm["y",FontSize->20], StyleForm["arcsin(y)",FontSize->20]}]

Gałęzie

Plot[{ArcSin[x],ArcSin[-x]+Pi,ArcSin[x]+2Pi,ArcSin[-x]-Pi}, {x, -1, 1}, ImageSize -> 400,AspectRatio->2,PlotStyle->{Red,Automatic,Automatic,Automatic}, AxesLabel -> {StyleForm["y", FontSize -> 20], StyleForm["arcsin(y)", FontSize -> 20]}]

Symetria

Plot[{ArcSin[x],Sin[x],x},{x,-Pi/2,Pi/2},ImageSize->400,AxesLabel->{StyleForm["x",FontSize->20], StyleForm["sin(x), arcsin(x)",FontSize->20]},AspectRatio->1,PlotStyle->{Blue,Red,Dashed}]

Arcus cosinus

Show[Plot[{Cos[x]},{x,-7,10},AspectRatio->Pi/15,ImageSize->800],
Plot[{Cos[x]},{x,0,Pi},PlotStyle->Red],AxesLabel->{StyleForm["x",FontSize->20], StyleForm["cos(x)",FontSize->20]}]

Plot[{ArcCos[x]},{x,-1,1},ImageSize->400,PlotStyle->Red,AxesLabel->{StyleForm["y",FontSize->20], StyleForm["arccos(y)",FontSize->20]}]

Show[Plot[{ArcCos[x],x},{x,-1,1},PlotStyle->{Blue,Dashed}],Plot[{Cos[x],x},{x,0,Pi},PlotStyle->{Red,Dashed}],ImageSize->400,AxesLabel->{StyleForm["x",FontSize->20], StyleForm["cos(x), arccos(x)",FontSize->20]},AspectRatio->1,PlotRange->{{-1,Pi},{-1,Pi}}]

Arcus tangens

Show[Plot[{Tan[x]},{x,-7,10},AspectRatio->.3,ImageSize->800],
Plot[{Tan[x]},{x,-Pi/2,Pi/2},PlotStyle->Red],PlotRange->{-5,5},AxesLabel->{StyleForm["x",FontSize->20], StyleForm["tg(x)",FontSize->20]}]

Plot[{ArcTan[x]},{x,-10,10},AspectRatio->.4,ImageSize->600,PlotStyle->Red,AxesLabel->{StyleForm["y",FontSize->20], StyleForm["arctg(y)",FontSize->20]}]

Plot[{ArcTan[x],ArcTan[x]+Pi,ArcTan[x]-Pi,ArcTan[x]+2Pi}, {x, -10, 10}, AspectRatio -> 1, ImageSize -> 600, PlotStyle -> {Red,Automatic,Automatic,Automatic}, AxesLabel -> {StyleForm["y", FontSize -> 20], StyleForm["arctg(y)", FontSize -> 20]}]

Arcus cotangens

Show[Plot[{Cot[x]},{x,-7,10},AspectRatio->.3,ImageSize->800],
Plot[{Cot[x]},{x,0,Pi},PlotStyle->Red,PlotRange->{-5,5}],AxesLabel->{StyleForm["x",FontSize->20], StyleForm["ctg(x)",FontSize->20]}]

Show[Plot[{ArcCot[x]},{x,-3,10},AspectRatio->.4,ImageSize->600,PlotStyle->Red],
Plot[{ArcCot[x]+Pi},{x,-10,0},AspectRatio->.4,ImageSize->600,PlotStyle->Red],PlotRange->{0,Pi},AxesOrigin->{0,0},AxesLabel->{StyleForm["y",FontSize->20], StyleForm["arcctg(y)",FontSize->20]}]