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 ArcSin

 http://functions.wolfram.com/01.12.27.1349.01

 Input Form

 ArcSin[Sqrt[z^2 + 1]] == Pi/2 - (Sqrt[-z^4]/z^2) ArcCosh[Sqrt[z^2 + 1]]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["ArcSin", "[", SqrtBox[RowBox[List[SuperscriptBox["z", "2"], "+", "1"]]], "]"]], "\[Equal]", RowBox[List[FractionBox["\[Pi]", "2"], "-", RowBox[List[FractionBox[SqrtBox[RowBox[List["-", SuperscriptBox["z", "4"]]]], SuperscriptBox["z", "2"]], RowBox[List["ArcCosh", "[", SqrtBox[RowBox[List[SuperscriptBox["z", "2"], "+", "1"]]], "]"]], " "]]]]]]]]

 MathML Form

 sin - 1 ( z 2 + 1 ) π 2 - - z 4 z 2 cosh - 1 ( z 2 + 1 ) z 2 1 1 2 2 -1 -1 -1 z 4 1 2 z 2 -1 z 2 1 1 2 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcSin", "[", SqrtBox[RowBox[List[SuperscriptBox["z_", "2"], "+", "1"]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["\[Pi]", "2"], "-", FractionBox[RowBox[List[SqrtBox[RowBox[List["-", SuperscriptBox["z", "4"]]]], " ", RowBox[List["ArcCosh", "[", SqrtBox[RowBox[List[SuperscriptBox["z", "2"], "+", "1"]]], "]"]]]], SuperscriptBox["z", "2"]]]]]]]]

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

 2003-08-21