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 ArcSin

 http://functions.wolfram.com/01.12.27.0630.01

 Input Form

 ArcSin[Sqrt[-z^2]/Sqrt[-z^2 - 1]] == (-z) Sqrt[z^(-2)] ArcTan[1/z] + Pi/2

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["ArcSin", "[", FractionBox[SqrtBox[RowBox[List["-", SuperscriptBox["z", "2"]]]], SqrtBox[RowBox[List[RowBox[List["-", SuperscriptBox["z", "2"]]], "-", "1"]]]], "]"]], "\[Equal]", RowBox[List[RowBox[List[RowBox[List["-", "z"]], SqrtBox[SuperscriptBox["z", RowBox[List["-", "2"]]]], RowBox[List["ArcTan", "[", FractionBox["1", "z"], "]"]]]], "+", FractionBox["\[Pi]", "2"]]]]]]]

 MathML Form

 sin - 1 ( - z 2 - z 2 - 1 ) π 2 - z 1 z 2 tan - 1 ( 1 z ) -1 z 2 1 2 -1 z 2 -1 1 2 -1 2 -1 -1 z 1 z 2 -1 1 2 1 z -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcSin", "[", FractionBox[SqrtBox[RowBox[List["-", SuperscriptBox["z_", "2"]]]], SqrtBox[RowBox[List[RowBox[List["-", SuperscriptBox["z_", "2"]]], "-", "1"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["-", "z"]], " ", SqrtBox[FractionBox["1", SuperscriptBox["z", "2"]]], " ", RowBox[List["ArcTan", "[", FractionBox["1", "z"], "]"]]]], "+", FractionBox["\[Pi]", "2"]]]]]]]

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

 2003-08-21