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 ArcSin

 http://functions.wolfram.com/01.12.27.0688.01

 Input Form

 ArcSin[z] == Pi/2 + ArcCot[Sqrt[z^2/(1 - z^2)]] /; Element[I z, Reals] && 0 < I z < 1

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcSin", "[", "z", "]"]], "\[Equal]", RowBox[List[FractionBox["\[Pi]", "2"], "+", RowBox[List["ArcCot", "[", SqrtBox[FractionBox[SuperscriptBox["z", "2"], RowBox[List["1", "-", SuperscriptBox["z", "2"]]]]], "]"]]]]]], "/;", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "z"]], "\[Element]", "Reals"]], "\[And]", RowBox[List["0", "<", RowBox[List["\[ImaginaryI]", " ", "z"]], "<", "1"]]]], ")"]]]]]]

 MathML Form

 sin - 1 ( z ) cot - 1 ( z 2 1 - z 2 ) + π 2 /; ( z 0 < z < 1 ) Condition z z 2 1 -1 z 2 -1 1 2 2 -1 z 0 z 1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcSin", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["\[Pi]", "2"], "+", RowBox[List["ArcCot", "[", SqrtBox[FractionBox[SuperscriptBox["z", "2"], RowBox[List["1", "-", SuperscriptBox["z", "2"]]]]], "]"]]]], "/;", RowBox[List[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "z"]], "\[Element]", "Reals"]], "&&", RowBox[List["0", "<", RowBox[List["\[ImaginaryI]", " ", "z"]], "<", "1"]]]]]]]]]]

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

 2003-08-21