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 ArcSin

 http://functions.wolfram.com/01.12.27.0424.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-08-21