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ArcCos




Mathematica Notation

Traditional Notation









Elementary Functions > ArcCos[z] > Representations through equivalent functions > With related functions > Involving sech-1 > Involving cos-1(z) > Involving cos-1(z) and sech-1(1/2z (1-z2)1/2)





http://functions.wolfram.com/01.13.27.2310.01









  


  








Input Form





ArcCos[z] == (Pi/4) (2 - Sqrt[-(1/z)] Sqrt[-z] Sqrt[1/(1 - Sqrt[2] z)] Sqrt[1 - Sqrt[2] z] + Sqrt[1/z] Sqrt[z] Sqrt[1/(1 + Sqrt[2] z)] Sqrt[1 + Sqrt[2] z] - Sqrt[z^2]/z - Sqrt[-z^2 + z^4]/ (z Sqrt[-1 + z^2])) + ((Sqrt[-z^2] Sqrt[-1 + z^2] Sqrt[-1 + 2 z^2])/ (2 Sqrt[1 - 2 z^2] Sqrt[-z^2 + z^4])) (Pi/2 - (Sqrt[1 - 2 z Sqrt[1 - z^2]]/Sqrt[2 z Sqrt[1 - z^2] - 1]) ArcSech[1/(2 z Sqrt[1 - z^2])])








Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCos", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["1", "4"], " ", "\[Pi]", " ", RowBox[List["(", RowBox[List["2", "-", RowBox[List[SqrtBox[RowBox[List["-", FractionBox["1", "z"]]]], " ", SqrtBox[RowBox[List["-", "z"]]], " ", SqrtBox[FractionBox["1", RowBox[List["1", "-", RowBox[List[SqrtBox["2"], " ", "z"]]]]]], " ", SqrtBox[RowBox[List["1", "-", RowBox[List[SqrtBox["2"], " ", "z"]]]]]]], "+", RowBox[List[SqrtBox[FractionBox["1", "z"]], " ", SqrtBox["z"], " ", SqrtBox[FractionBox["1", RowBox[List["1", "+", RowBox[List[SqrtBox["2"], " ", "z"]]]]]], " ", SqrtBox[RowBox[List["1", "+", RowBox[List[SqrtBox["2"], " ", "z"]]]]]]], "-", FractionBox[SqrtBox[SuperscriptBox["z", "2"]], "z"], "-", FractionBox[SqrtBox[RowBox[List[RowBox[List["-", SuperscriptBox["z", "2"]]], "+", SuperscriptBox["z", "4"]]]], RowBox[List["z", " ", SqrtBox[RowBox[List[RowBox[List["-", "1"]], "+", SuperscriptBox["z", "2"]]]]]]]]], ")"]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SqrtBox[RowBox[List["-", SuperscriptBox["z", "2"]]]], " ", SqrtBox[RowBox[List[RowBox[List["-", "1"]], "+", SuperscriptBox["z", "2"]]]], " ", SqrtBox[RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["2", " ", SuperscriptBox["z", "2"]]]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[FractionBox["\[Pi]", "2"], "-", FractionBox[RowBox[List[SqrtBox[RowBox[List["1", "-", RowBox[List["2", " ", "z", " ", SqrtBox[RowBox[List["1", "-", SuperscriptBox["z", "2"]]]]]]]]], " ", RowBox[List["ArcSech", "[", FractionBox["1", RowBox[List["2", " ", "z", " ", SqrtBox[RowBox[List["1", "-", SuperscriptBox["z", "2"]]]]]]], "]"]]]], SqrtBox[RowBox[List[RowBox[List["2", " ", "z", " ", SqrtBox[RowBox[List["1", "-", SuperscriptBox["z", "2"]]]]]], "-", "1"]]]]]], ")"]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["1", "-", RowBox[List["2", " ", SuperscriptBox["z", "2"]]]]]], " ", SqrtBox[RowBox[List[RowBox[List["-", SuperscriptBox["z", "2"]]], "+", SuperscriptBox["z", "4"]]]]]]]]]]]]]


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





2003-08-21