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 ArcSin

 http://functions.wolfram.com/01.12.27.0404.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-08-21