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Sin




Mathematica Notation

Traditional Notation









Elementary Functions > Sin[z] > Transformations > Addition formulas





http://functions.wolfram.com/01.06.16.0087.01









  


  








Input Form





Sin[a - I b] == Sin[a] Cosh[b] - I Cos[a] Sinh[b]








Standard Form





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








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> &#8289; </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> b </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> cosh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> b </mi> <mo> ) </mo> </mrow> </mrow> <mtext> </mtext> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> sinh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> b </mi> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <sin /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> b </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <sin /> <ci> a </ci> </apply> <apply> <cosh /> <ci> b </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <cos /> <ci> a </ci> </apply> <apply> <sinh /> <ci> b </ci> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Sin", "[", RowBox[List["a_", "-", RowBox[List["\[ImaginaryI]", " ", "b_"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["Sin", "[", "a", "]"]], " ", RowBox[List["Cosh", "[", "b", "]"]]]], "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["Cos", "[", "a", "]"]], " ", RowBox[List["Sinh", "[", "b", "]"]]]]]]]]]]


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





2001-10-29