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 ArcSin

 http://functions.wolfram.com/01.12.27.0739.01

 Input Form

 ArcSin[z] == Pi - 2 ArcCot[z/(1 + Sqrt[1 - z^2])] /; Inequality[-(Pi/2), LessEqual, Arg[z], Less, Pi/2]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcSin", "[", "z", "]"]], "\[Equal]", RowBox[List["\[Pi]", " ", "-", RowBox[List["2", " ", RowBox[List["ArcCot", "[", FractionBox["z", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", SuperscriptBox["z", "2"]]]]]]], "]"]]]]]]]], "/;", RowBox[List[RowBox[List["-", FractionBox["\[Pi]", "2"]]], "\[LessEqual]", RowBox[List["Arg", "[", "z", "]"]], "<", FractionBox["\[Pi]", "2"]]]]]]]

 MathML Form

 sin - 1 ( z ) π - 2 cot - 1 ( z 1 + 1 - z 2 ) /; - π 2 arg ( z ) < π 2 Condition z -1 2 z 1 1 -1 z 2 1 2 -1 Inequality -1 2 -1 z 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcSin", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["\[Pi]", "-", RowBox[List["2", " ", RowBox[List["ArcCot", "[", FractionBox["z", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", SuperscriptBox["z", "2"]]]]]]], "]"]]]]]], "/;", RowBox[List[RowBox[List["-", FractionBox["\[Pi]", "2"]]], "\[LessEqual]", RowBox[List["Arg", "[", "z", "]"]], "<", FractionBox["\[Pi]", "2"]]]]]]]]]

 Date Added to functions.wolfram.com (modification date)

 2003-08-21