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 ArcSin

 http://functions.wolfram.com/01.12.27.0462.01

 Input Form

 ArcSin[z] == -((3 Pi)/2) + 2 ArcTan[Sqrt[(1 - z)/(1 + z)]] /; Element[z, Reals] && z < -1

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcSin", "[", "z", "]"]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["3", "\[Pi]"]], "2"]]], "+", RowBox[List["2", " ", RowBox[List["ArcTan", "[", SqrtBox[FractionBox[RowBox[List["1", "-", "z"]], RowBox[List["1", "+", "z"]]]], "]"]]]]]]]], "/;", " ", RowBox[List["(", RowBox[List[RowBox[List["z", "\[Element]", "Reals"]], "\[And]", RowBox[List["z", "<", RowBox[List["-", "1"]]]]]], ")"]]]]]]

 MathML Form

 sin - 1 ( z ) 2 tan - 1 ( 1 - z z + 1 ) - 3 π 2 /; ( z z < - 1 ) Condition z 2 1 -1 z z 1 -1 1 2 -1 3 2 -1 z z -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcSin", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", RowBox[List["(", RowBox[List["3", " ", "\[Pi]"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["ArcTan", "[", SqrtBox[FractionBox[RowBox[List["1", "-", "z"]], RowBox[List["1", "+", "z"]]]], "]"]]]]]], "/;", RowBox[List[RowBox[List["z", "\[Element]", "Reals"]], "&&", RowBox[List["z", "<", RowBox[List["-", "1"]]]]]]]]]]]]

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

 2003-08-21