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 ArcSin

 http://functions.wolfram.com/01.12.27.0360.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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