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ArcCos




Mathematica Notation

Traditional Notation









Elementary Functions > ArcCos[z] > Representations through equivalent functions > With inverse function > Involving cos-1(sin(z))





http://functions.wolfram.com/01.13.27.2513.01









  


  








Input Form





ArcCos[Sin[z]] == (1/2) (Pi - (-1)^Floor[-(1/2) + Re[z]/Pi] Pi + (-1)^Floor[-(1/2) + Re[z]/Pi] (Pi - 2 z + 2 Pi Floor[-(1/2) + Re[z]/Pi]) (-1 + (1 + (-1)^(Floor[1/2 - Re[z]/Pi] + Floor[-(1/2) + Re[z]/Pi])) UnitStep[-Im[z]]))








Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCos", "[", RowBox[List["Sin", "[", "z_", "]"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["\[Pi]", "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["Floor", "[", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "+", FractionBox[RowBox[List["Re", "[", "z", "]"]], "\[Pi]"]]], "]"]]], " ", "\[Pi]"]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["Floor", "[", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "+", FractionBox[RowBox[List["Re", "[", "z", "]"]], "\[Pi]"]]], "]"]]], " ", RowBox[List["(", RowBox[List["\[Pi]", "-", RowBox[List["2", " ", "z"]], "+", RowBox[List["2", " ", "\[Pi]", " ", RowBox[List["Floor", "[", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "+", FractionBox[RowBox[List["Re", "[", "z", "]"]], "\[Pi]"]]], "]"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List[RowBox[List["(", RowBox[List["1", "+", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List[RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[RowBox[List["Re", "[", "z", "]"]], "\[Pi]"]]], "]"]], "+", RowBox[List["Floor", "[", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "+", FractionBox[RowBox[List["Re", "[", "z", "]"]], "\[Pi]"]]], "]"]]]]]]], ")"]], " ", RowBox[List["UnitStep", "[", RowBox[List["-", RowBox[List["Im", "[", "z", "]"]]]], "]"]]]]]], ")"]]]]]], ")"]]]]]]]]


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





2007-05-02