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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(2 (z2-1)1/2/z2) > Involving cos-1(2 (z2-1)1/2/z2) and cos-1(1/z)





http://functions.wolfram.com/01.13.16.0085.01









  


  










Input Form





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










Standard Form





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MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msup> <mi> cos </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mn> 1 </mn> </mrow> </msqrt> </mrow> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mfrac> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mfrac> <mrow> <mi> &#960; </mi> <mo> &#8290; </mo> <msqrt> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </msqrt> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mfrac> <msqrt> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </msqrt> <mi> z </mi> </mfrac> <mo> - </mo> <mrow> <msqrt> <mfrac> <mi> z </mi> <mrow> <mi> z </mi> <mo> + </mo> <msqrt> <mn> 2 </mn> </msqrt> </mrow> </mfrac> </msqrt> <mo> &#8290; </mo> <msqrt> <mfrac> <mrow> <mi> z </mi> <mo> + </mo> <msqrt> <mn> 2 </mn> </msqrt> </mrow> <mi> z </mi> </mfrac> </msqrt> </mrow> <mo> + </mo> <mrow> <msqrt> <mfrac> <mrow> <mi> z </mi> <mo> - </mo> <msqrt> <mn> 2 </mn> </msqrt> </mrow> <mi> z </mi> </mfrac> </msqrt> <mo> &#8290; 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Rule Form





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










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





2003-08-21





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