html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 Tan

 http://functions.wolfram.com/01.08.03.0021.01

 Input Form

 Tan[(2 Pi)/7] == ((1 - 3 I Sqrt[3])^(1/3) (4 7^(5/6) (2 - 6 I Sqrt[3])^(1/3) + 2^(1/3) (4 Sqrt[7] (14 - I Sqrt[7] - 3 Sqrt[21])^(1/3) + (I + Sqrt[3]) (14 - I Sqrt[7] - 3 Sqrt[21])^(2/3) (28 + 2 I Sqrt[7] + 6 Sqrt[21])^(1/3) + 2 I (14 + I Sqrt[7] + 3 Sqrt[21])^(1/3) (I Sqrt[7] - Sqrt[21] + (28 - 84 I Sqrt[3])^(1/3)))))/ (4 (7 2^(2/3) (1 - 3 I Sqrt[3])^(1/3) - 14^(1/3) (1 - 3 I Sqrt[3])^(2/3) + 7^(2/3) (1 - 3 I Sqrt[3])))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Tan", "[", FractionBox[RowBox[List["2", " ", "\[Pi]"]], "7"], "]"]], "\[Equal]", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", RowBox[List["3", " ", "\[ImaginaryI]", " ", SqrtBox["3"]]]]], ")"]], RowBox[List["1", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["4", " ", SuperscriptBox["7", RowBox[List["5", "/", "6"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["2", "-", RowBox[List["6", " ", "\[ImaginaryI]", " ", SqrtBox["3"]]]]], ")"]], RowBox[List["1", "/", "3"]]]]], "+", RowBox[List[SuperscriptBox["2", RowBox[List["1", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["4", " ", SqrtBox["7"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["14", "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox["7"]]], "-", RowBox[List["3", " ", SqrtBox["21"]]]]], ")"]], RowBox[List["1", "/", "3"]]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["\[ImaginaryI]", "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["14", "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox["7"]]], "-", RowBox[List["3", " ", SqrtBox["21"]]]]], ")"]], RowBox[List["2", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["28", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", SqrtBox["7"]]], "+", RowBox[List["6", " ", SqrtBox["21"]]]]], ")"]], RowBox[List["1", "/", "3"]]]]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List["14", "+", RowBox[List["\[ImaginaryI]", " ", SqrtBox["7"]]], "+", RowBox[List["3", " ", SqrtBox["21"]]]]], ")"]], RowBox[List["1", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", SqrtBox["7"]]], "-", SqrtBox["21"], "+", SuperscriptBox[RowBox[List["(", RowBox[List["28", "-", RowBox[List["84", " ", "\[ImaginaryI]", " ", SqrtBox["3"]]]]], ")"]], RowBox[List["1", "/", "3"]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], ")"]], "/", RowBox[List["(", RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["7", " ", SuperscriptBox["2", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", RowBox[List["3", " ", "\[ImaginaryI]", " ", SqrtBox["3"]]]]], ")"]], RowBox[List["1", "/", "3"]]]]], "-", RowBox[List[SuperscriptBox["14", RowBox[List["1", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", RowBox[List["3", " ", "\[ImaginaryI]", " ", SqrtBox["3"]]]]], ")"]], RowBox[List["2", "/", "3"]]]]], "+", RowBox[List[SuperscriptBox["7", RowBox[List["2", "/", "3"]]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["3", " ", "\[ImaginaryI]", " ", SqrtBox["3"]]]]], ")"]]]]]], ")"]]]], ")"]]]]]]]]

 MathML Form

 tan ( 2 π 7 ) ( 1 - 3 3 3 ( 4 7 5 / 6 2 - 6 3 3 + 2 3 ( 2 ( 28 - 84 3 3 + 7 - 21 ) 14 + 7 + 3 21 3 + 4 7 14 - 7 - 3 21 3 + ( + 3 ) 28 + 2 7 + 6 21 3 ( 14 - 7 - 3 21 ) 2 / 3 ) ) ) / ( 4 ( 7 2 2 / 3 1 - 3 3 3 - 14 3 ( 1 - 3 3 ) 2 / 3 + 7 2 / 3 ( 1 - 3 3 ) ) ) 2 7 -1 1 -1 3 3 1 2 1 3 4 7 5 6 2 -1 6 3 1 2 1 3 2 1 3 2 28 -1 84 3 1 2 1 3 7 1 2 -1 21 1 2 14 7 1 2 3 21 1 2 1 3 4 7 1 2 14 -1 7 1 2 -1 3 21 1 2 1 3 3 1 2 28 2 7 1 2 6 21 1 2 1 3 14 -1 7 1 2 -1 3 21 1 2 2 3 4 7 2 2 3 1 -1 3 3 1 2 1 3 -1 14 1 3 1 -1 3 3 1 2 2 3 7 2 3 1 -1 3 3 1 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Tan", "[", FractionBox[RowBox[List["2", " ", "\[Pi]"]], "7"], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", RowBox[List["3", " ", "\[ImaginaryI]", " ", SqrtBox["3"]]]]], ")"]], RowBox[List["1", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["4", " ", SuperscriptBox["7", RowBox[List["5", "/", "6"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["2", "-", RowBox[List["6", " ", "\[ImaginaryI]", " ", SqrtBox["3"]]]]], ")"]], RowBox[List["1", "/", "3"]]]]], "+", RowBox[List[SuperscriptBox["2", RowBox[List["1", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["4", " ", SqrtBox["7"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["14", "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox["7"]]], "-", RowBox[List["3", " ", SqrtBox["21"]]]]], ")"]], RowBox[List["1", "/", "3"]]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["\[ImaginaryI]", "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["14", "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox["7"]]], "-", RowBox[List["3", " ", SqrtBox["21"]]]]], ")"]], RowBox[List["2", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["28", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", SqrtBox["7"]]], "+", RowBox[List["6", " ", SqrtBox["21"]]]]], ")"]], RowBox[List["1", "/", "3"]]]]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List["14", "+", RowBox[List["\[ImaginaryI]", " ", SqrtBox["7"]]], "+", RowBox[List["3", " ", SqrtBox["21"]]]]], ")"]], RowBox[List["1", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", SqrtBox["7"]]], "-", SqrtBox["21"], "+", SuperscriptBox[RowBox[List["(", RowBox[List["28", "-", RowBox[List["84", " ", "\[ImaginaryI]", " ", SqrtBox["3"]]]]], ")"]], RowBox[List["1", "/", "3"]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["7", " ", SuperscriptBox["2", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", RowBox[List["3", " ", "\[ImaginaryI]", " ", SqrtBox["3"]]]]], ")"]], RowBox[List["1", "/", "3"]]]]], "-", RowBox[List[SuperscriptBox["14", RowBox[List["1", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", RowBox[List["3", " ", "\[ImaginaryI]", " ", SqrtBox["3"]]]]], ")"]], RowBox[List["2", "/", "3"]]]]], "+", RowBox[List[SuperscriptBox["7", RowBox[List["2", "/", "3"]]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["3", " ", "\[ImaginaryI]", " ", SqrtBox["3"]]]]], ")"]]]]]], ")"]]]]]]]]]

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

 2001-10-29