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ArcCos






Mathematica Notation

Traditional Notation









Elementary Functions > ArcCos[z] > Transformations > Transformations and argument simplifications > Argument involving basic arithmetic operations > Involving cos-1((z-(z2-1)1/2)1/2/(2z)1/2) > Involving cos-1((z-(z2-1)1/2)1/2/(2z)1/2) and cos-1(1/z)





http://functions.wolfram.com/01.13.16.0097.01









  


  










Input Form





ArcCos[Sqrt[z - Sqrt[z^2 - 1]]/Sqrt[2 z]] == (1/2) Sqrt[I/z] Sqrt[1/z] Sqrt[(-I) z] Sqrt[z] Sqrt[1/(1 + z)] Sqrt[1 + z] ArcCos[1/z] + (1/4) Pi (2 - Sqrt[I/z] Sqrt[1/z] Sqrt[(-I) z] Sqrt[z] Sqrt[1/(1 + z)] Sqrt[1 + z] + (Sqrt[1/z] Sqrt[1/(1 + z)] (-z + Sqrt[z^2]))/Sqrt[z/(1 + 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", "[", FractionBox[SqrtBox[RowBox[List["z_", "-", SqrtBox[RowBox[List[SuperscriptBox["z_", "2"], "-", "1"]]]]]], SqrtBox[RowBox[List["2", " ", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", SqrtBox[FractionBox["\[ImaginaryI]", "z"]], " ", SqrtBox[FractionBox["1", "z"]], " ", SqrtBox[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "z"]]], " ", SqrtBox["z"], " ", SqrtBox[FractionBox["1", RowBox[List["1", "+", "z"]]]], " ", SqrtBox[RowBox[List["1", "+", "z"]]], " ", RowBox[List["ArcCos", "[", FractionBox["1", "z"], "]"]]]], "+", RowBox[List[FractionBox["1", "4"], " ", "\[Pi]", " ", RowBox[List["(", RowBox[List["2", "-", RowBox[List[SqrtBox[FractionBox["\[ImaginaryI]", "z"]], " ", SqrtBox[FractionBox["1", "z"]], " ", SqrtBox[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "z"]]], " ", SqrtBox["z"], " ", SqrtBox[FractionBox["1", RowBox[List["1", "+", "z"]]]], " ", SqrtBox[RowBox[List["1", "+", "z"]]]]], "+", FractionBox[RowBox[List[SqrtBox[FractionBox["1", "z"]], " ", SqrtBox[FractionBox["1", RowBox[List["1", "+", "z"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "z"]], "+", SqrtBox[SuperscriptBox["z", "2"]]]], ")"]]]], SqrtBox[FractionBox["z", RowBox[List["1", "+", "z"]]]]]]], ")"]]]]]]]]]]










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





2003-08-21





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