Inverse trigonometric functions as implemented in Mathematica

2015 - 03 - 10

Principal branch of Arccot(x)  differs  from function range of ArcCot[x]

pr = Plot[ArcCot[x],{x,-7,7},AxesLabel->{"x",None}, PlotLabel -> "ArcCot[x]", Ticks -> {Automatic,π{-1/2,0,1/2}},PlotRange ->{{-7,7},{-3.2/2,3.2/2}}]

fc[x_]= If[x <0, π + ArcCot[x],ArcCot[x]]

pl = Plot[fc[x],{x,-7,7},AxesLabel->{"x",None}, PlotLabel -> "arccot(x)",
Ticks -> {Automatic,π{0,1/2,1}},PlotRange ->{{-7,7},{0,3.2}}]

Show[GraphicsRow[{pl,pr}]]

Arcsin[x]

Plot[ArcSin[x],{x,-1,1},AxesLabel->{"x",None}, PlotLabel -> "arcsin(x)",
Ticks -> {Automatic,π/2{-1,1}}]

Arccos[x]

Plot[ArcCos[x],{x,-1,1},AxesLabel->{"x",None}, PlotLabel -> "arcsin(x)",
Ticks -> {Automatic,π{0,1/2,1}}]

Arctan[x]

Plot[ArcTan[x],{x,-7,7},AxesLabel->{"x",None}, PlotLabel -> "ArcCot[x]", Ticks -> {Automatic,π{-1/2,0,1/2}},PlotRange ->{{-7,7},{-3.2/2,3.2/2}}]