Sine: Representations through more general functions (formula 01.06.26.0079)

Sin

$Mathematica Notation$

Elementary Functions

Sin[z]

Representations through more general functions

Through other functions

Involving Jacobi functions

http://functions.wolfram.com/01.06.26.0079.01

Input Form

Sin[z] == 1/JacobiNC[Pi/2 - z, 0]

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["Sin", "[", "z", "]"]], "\[Equal]", FractionBox["1", RowBox[List["JacobiNC", "[", RowBox[List[RowBox[List[FractionBox["\[Pi]", "2"], "-", "z"]], ",", "0"]], "]"]]]]]]]

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> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mfrac> <mn> 1 </mn> <mrow> <mi> nc </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mfrac> <mi> π </mi> <mn> 2 </mn> </mfrac> <mo> - </mo> <mi> z </mi> </mrow> <mo> ❘ </mo> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <sin /> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <ci> JacobiNC </ci> <apply> <plus /> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 0 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Sin", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", FractionBox["1", RowBox[List["JacobiNC", "[", RowBox[List[RowBox[List[FractionBox["\[Pi]", "2"], "-", "z"]], ",", "0"]], "]"]]]]]]]

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

2001-10-29