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ArcSin




Mathematica Notation

Traditional Notation









Elementary Functions > ArcSin[z] > Representations through equivalent functions > With related functions > Involving tan-1 > Involving sin-1(1+z/1-z) > Involving sin-1(1+z/1-z) and tan-1((-z)1/2)





http://functions.wolfram.com/01.12.27.0510.01









  


  








Input Form





ArcSin[(1 + z)/(1 - z)] == 2 ArcTan[Sqrt[-z]] - (3 Pi)/2 /; Element[z, Reals] && z > 1








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcSin", "[", FractionBox[RowBox[List["1", "+", "z"]], RowBox[List["1", "-", "z"]]], "]"]], "\[Equal]", RowBox[List[RowBox[List["2", RowBox[List["ArcTan", "[", SqrtBox[RowBox[List["-", "z"]]], "]"]]]], "-", FractionBox[RowBox[List["3", "\[Pi]"]], "2"]]]]], "/;", " ", RowBox[List["(", RowBox[List[RowBox[List["z", "\[Element]", "Reals"]], "\[And]", RowBox[List["z", ">", "1"]]]], ")"]]]]]]








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> <msup> <mi> sin </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mfrac> <mrow> <mn> 1 </mn> <mo> + </mo> <mi> z </mi> </mrow> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> </mfrac> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <msup> <mi> tan </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <msqrt> <mrow> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mfrac> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mn> 2 </mn> </mfrac> </mrow> </mrow> <mo> /; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> &#8712; </mo> <mi> &#8477; </mi> </mrow> <mo> &#8743; </mo> <mrow> <mi> z </mi> <mo> &gt; </mo> <mn> 1 </mn> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <arcsin /> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <ci> z </ci> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <arctan /> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3 </cn> <pi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <in /> <ci> z </ci> <ci> &#8477; </ci> </apply> <apply> <gt /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcSin", "[", FractionBox[RowBox[List["1", "+", "z_"]], RowBox[List["1", "-", "z_"]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["2", " ", RowBox[List["ArcTan", "[", SqrtBox[RowBox[List["-", "z"]]], "]"]]]], "-", FractionBox[RowBox[List["3", " ", "\[Pi]"]], "2"]]], "/;", RowBox[List[RowBox[List["z", "\[Element]", "Reals"]], "&&", RowBox[List["z", ">", "1"]]]]]]]]]]


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





2003-08-21