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Sin




Mathematica Notation

Traditional Notation









Elementary Functions > Sin[z] > Transformations > Some functions of arguments





http://functions.wolfram.com/01.06.16.0164.01









  


  








Input Form





Sin[a (b z^4)^(1/4)] == ((b^(1/4) z)/(2 (b z^4)^(3/4))) ((Sqrt[b] z^2 + Sqrt[b z^4]) Sin[a b^(1/4) z] + (Sqrt[b] z^2 - Sqrt[b z^4]) Sinh[a b^(1/4) z])








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Sin", "[", RowBox[List["a", " ", SuperscriptBox[RowBox[List["(", RowBox[List["b", " ", SuperscriptBox["z", "4"]]], ")"]], RowBox[List["1", "/", "4"]]]]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["b", RowBox[List["1", "/", "4"]]], " ", "z"]], RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List["b", " ", SuperscriptBox["z", "4"]]], ")"]], RowBox[List["3", "/", "4"]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[SqrtBox["b"], " ", SuperscriptBox["z", "2"]]], "+", SqrtBox[RowBox[List["b", " ", SuperscriptBox["z", "4"]]]]]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List["a", " ", SuperscriptBox["b", RowBox[List["1", "/", "4"]]], " ", "z"]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[SqrtBox["b"], " ", SuperscriptBox["z", "2"]]], "-", SqrtBox[RowBox[List["b", " ", SuperscriptBox["z", "4"]]]]]], ")"]], " ", RowBox[List["Sinh", "[", RowBox[List["a", " ", SuperscriptBox["b", RowBox[List["1", "/", "4"]]], " ", "z"]], "]"]]]]]], ")"]]]]]]]]








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> &#8290; </mo> <mroot> <mrow> <mi> b </mi> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mn> 4 </mn> </mroot> </mrow> <mo> ) </mo> </mrow> <mo> &#63449; </mo> <mrow> <mfrac> <mrow> <mroot> <mi> b </mi> <mn> 4 </mn> </mroot> <mo> &#8290; </mo> <mi> z </mi> <mtext> </mtext> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 4 </mn> </mrow> </msup> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <msqrt> <mi> b </mi> </msqrt> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <msqrt> <mrow> <mi> b </mi> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mroot> <mi> b </mi> <mn> 4 </mn> </mroot> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <msqrt> <mi> b </mi> </msqrt> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <msqrt> <mrow> <mi> b </mi> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> sinh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mroot> <mi> b </mi> <mn> 4 </mn> </mroot> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <sin /> <apply> <times /> <ci> a </ci> <apply> <power /> <apply> <times /> <ci> b </ci> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 4 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <apply> <power /> <ci> b </ci> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <ci> z </ci> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <times /> <ci> b </ci> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <cn type='rational'> 3 <sep /> 4 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> b </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <ci> b </ci> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <sin /> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> b </ci> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> b </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <times /> <ci> b </ci> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <sinh /> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> b </ci> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Sin", "[", RowBox[List["a_", " ", SuperscriptBox[RowBox[List["(", RowBox[List["b_", " ", SuperscriptBox["z_", "4"]]], ")"]], RowBox[List["1", "/", "4"]]]]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["b", RowBox[List["1", "/", "4"]]], " ", "z"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[SqrtBox["b"], " ", SuperscriptBox["z", "2"]]], "+", SqrtBox[RowBox[List["b", " ", SuperscriptBox["z", "4"]]]]]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List["a", " ", SuperscriptBox["b", RowBox[List["1", "/", "4"]]], " ", "z"]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[SqrtBox["b"], " ", SuperscriptBox["z", "2"]]], "-", SqrtBox[RowBox[List["b", " ", SuperscriptBox["z", "4"]]]]]], ")"]], " ", RowBox[List["Sinh", "[", RowBox[List["a", " ", SuperscriptBox["b", RowBox[List["1", "/", "4"]]], " ", "z"]], "]"]]]]]], ")"]]]], RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List["b", " ", SuperscriptBox["z", "4"]]], ")"]], RowBox[List["3", "/", "4"]]]]]]]]]]


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





2007-05-02