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 ArcTan

 http://functions.wolfram.com/01.15.03.0002.01

 Input Form

 ArcTan[x, y] == ArcTan[y/x] + (2 UnitStep[y] - 1) Pi /; Element[y, Reals] && Re[x] < 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcTan", "[", RowBox[List["x", ",", "y"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["ArcTan", "[", FractionBox["y", "x"], "]"]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", RowBox[List["UnitStep", "[", "y", "]"]]]], "-", "1"]], ")"]], "\[Pi]"]]]]]], "/;", RowBox[List[RowBox[List["Element", "[", RowBox[List["y", ",", "Reals"]], "]"]], "\[And]", RowBox[List[RowBox[List["Re", "[", "x", "]"]], "<", "0"]]]]]]]]

 MathML Form

 tan - 1 ( x , y ) tan - 1 ( y x ) + ( 2 θ ( y ) - 1 ) π /; y TagBox["\[DoubleStruckCapitalR]", Function[Reals]] Re ( x ) < 0 Condition x y y x -1 2 θ y -1 y x 0 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcTan", "[", RowBox[List["x_", ",", "y_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["ArcTan", "[", FractionBox["y", "x"], "]"]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", " ", RowBox[List["UnitStep", "[", "y", "]"]]]], "-", "1"]], ")"]], " ", "\[Pi]"]]]], "/;", RowBox[List[RowBox[List["y", "\[Element]", "Reals"]], "&&", RowBox[List[RowBox[List["Re", "[", "x", "]"]], "<", "0"]]]]]]]]]]

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

 2001-10-29