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 ArcSin

 http://functions.wolfram.com/01.12.27.0116.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcSin", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["ArcSec", "[", FractionBox["1", SqrtBox[RowBox[List["1", "-", SuperscriptBox["z", "2"]]]]], "]"]], "/;", RowBox[List[RowBox[List["-", FractionBox["\[Pi]", "2"]]], "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", FractionBox["\[Pi]", "2"]]]]]]]]]

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

 2001-10-29