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Sin




Mathematica Notation

Traditional Notation









Elementary Functions > Sin[z] > Transformations > Products, sums, and powers of the direct function > Sums involving the direct function > Involving hyperbolic functions > Involving sinh





http://functions.wolfram.com/01.06.16.0122.01









  


  








Input Form





Sin[a] - I Sinh[b] == 2 Cos[(a + I b)/2] Sin[(a - I b)/2]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Sin", "[", "a", "]"]], "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["Sinh", "[", "b", "]"]]]]]], "\[Equal]", RowBox[List["2", " ", RowBox[List["Cos", "[", FractionBox[RowBox[List["a", "+", RowBox[List["\[ImaginaryI]", " ", "b"]]]], "2"], "]"]], " ", RowBox[List["Sin", "[", FractionBox[RowBox[List["a", "-", RowBox[List["\[ImaginaryI]", " ", "b"]]]], "2"], "]"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mi> sinh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> b </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> &#8520; </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> b </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <plus /> <apply> <sin /> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <sinh /> <ci> b </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <cos /> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <ci> a </ci> <apply> <times /> <ci> b </ci> <imaginaryi /> </apply> </apply> </apply> </apply> <apply> <sin /> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> b </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["Sin", "[", "a_", "]"]], "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["Sinh", "[", "b_", "]"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List["2", " ", RowBox[List["Cos", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["a", "+", RowBox[List["\[ImaginaryI]", " ", "b"]]]], ")"]]]], "]"]], " ", RowBox[List["Sin", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["a", "-", RowBox[List["\[ImaginaryI]", " ", "b"]]]], ")"]]]], "]"]]]]]]]]


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





2003-08-21