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Csc




Mathematica Notation

Traditional Notation









Elementary Functions > Csc[z] > Specific values > Values at fixed points





http://functions.wolfram.com/01.10.03.0038.01









  


  








Input Form





Csc[(4 Pi)/9] == 4/((-I + Sqrt[3]) ((1/2) I (I + Sqrt[3]))^(1/3) + ((-(1/2)) I (-I + Sqrt[3]))^(1/3) (I + Sqrt[3]))








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Csc", "[", FractionBox[RowBox[List["4", " ", "\[Pi]"]], "9"], "]"]], "\[Equal]", FractionBox["4", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[FractionBox["1", "2"], " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["\[ImaginaryI]", "+", SqrtBox["3"]]], ")"]]]], ")"]], RowBox[List["1", "/", "3"]]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], "+", SqrtBox["3"]]], ")"]]]], ")"]], RowBox[List["1", "/", "3"]]], " ", RowBox[List["(", RowBox[List["\[ImaginaryI]", "+", SqrtBox["3"]]], ")"]]]]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mi> csc </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mn> 9 </mn> </mfrac> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mfrac> <mn> 4 </mn> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> &#8520; </mi> <mo> + </mo> <msqrt> <mn> 3 </mn> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mroot> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> &#8520; </mi> </mrow> <mo> + </mo> <msqrt> <mn> 3 </mn> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 3 </mn> </mroot> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> &#8520; </mi> </mrow> <mo> + </mo> <msqrt> <mn> 3 </mn> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mroot> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> &#8520; </mi> <mo> + </mo> <msqrt> <mn> 3 </mn> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 3 </mn> </mroot> </mrow> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <csc /> <apply> <times /> <cn type='integer'> 4 </cn> <pi /> <apply> <power /> <cn type='integer'> 9 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <apply> <plus /> <apply> <times /> <apply> <plus /> <imaginaryi /> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <imaginaryi /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 3 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <imaginaryi /> <apply> <plus /> <imaginaryi /> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 3 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Csc", "[", FractionBox[RowBox[List["4", " ", "\[Pi]"]], "9"], "]"]], "]"]], "\[RuleDelayed]", FractionBox["4", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[FractionBox["1", "2"], " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["\[ImaginaryI]", "+", SqrtBox["3"]]], ")"]]]], ")"]], RowBox[List["1", "/", "3"]]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], "+", SqrtBox["3"]]], ")"]]]], ")"]], RowBox[List["1", "/", "3"]]], " ", RowBox[List["(", RowBox[List["\[ImaginaryI]", "+", SqrtBox["3"]]], ")"]]]]]]]]]]]


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





2001-10-29