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ArcSin






Mathematica Notation

Traditional Notation









Elementary Functions > ArcSin[z] > Complex characteristics > Signum value





http://functions.wolfram.com/01.12.19.0008.01









  


  










Input Form





Sign[ArcSin[x + I y]] == (ArcTan[-y + (x^4 + 2 x^2 (-1 + y^2) + (1 + y^2)^2)^(1/4) Cos[(1/2) ArcTan[1 - x^2 + y^2, -2 x y]], x + (x^4 + 2 x^2 (-1 + y^2) + (1 + y^2)^2)^(1/4) Sin[(1/2) ArcTan[1 - x^2 + y^2, -2 x y]]] - I Log[Sqrt[(y - (x^4 + 2 x^2 (-1 + y^2) + (1 + y^2)^2)^(1/4) Cos[(1/2) ArcTan[1 - x^2 + y^2, -2 x y]])^2 + (x + (x^4 + 2 x^2 (-1 + y^2) + (1 + y^2)^2)^(1/4) Sin[(1/2) ArcTan[1 - x^2 + y^2, -2 x y]])^2]])/ Sqrt[ArcTan[-y + (x^4 + 2 x^2 (-1 + y^2) + (1 + y^2)^2)^(1/4) Cos[(1/2) ArcTan[1 - x^2 + y^2, -2 x y]], x + (x^4 + 2 x^2 (-1 + y^2) + (1 + y^2)^2)^(1/4) Sin[(1/2) ArcTan[1 - x^2 + y^2, -2 x y]]]^2 + Log[Sqrt[(y - (x^4 + 2 x^2 (-1 + y^2) + (1 + y^2)^2)^(1/4) Cos[(1/2) ArcTan[1 - x^2 + y^2, -2 x y]])^2 + (x + (x^4 + 2 x^2 (-1 + y^2) + (1 + y^2)^2)^(1/4) Sin[(1/2) ArcTan[1 - x^2 + y^2, -2 x y]])^2]]^2]










Standard Form





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MathML Form







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1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mn> 4 </mn> </mroot> </mrow> <mo> + </mo> <mi> x </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> + </mo> <mrow> <msup> <mi> log </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mo> &#8730; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mi> y </mi> <mo> - </mo> <mrow> <mroot> <mrow> <msup> <mi> x </mi> <mn> 4 </mn> </msup> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> y </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> x </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <msup> <mrow> <mo> ( </mo> <mrow> <msup> <mi> y </mi> <mn> 2 </mn> </msup> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mn> 4 </mn> </mroot> <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> <msup> <mi> tan </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <msup> <mi> x </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <msup> <mi> y </mi> <mn> 2 </mn> </msup> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> &#8290; </mo> <mi> x </mi> <mo> &#8290; </mo> <mi> y </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> + </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <msup> <mi> tan </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <msup> <mi> x </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <msup> <mi> y </mi> <mn> 2 </mn> </msup> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mrow> <mrow> <mo> - 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type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <ci> x </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> y </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 4 </cn> </apply> </apply> <ci> x </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <ln /> <apply> <root /> <apply> <plus /> <apply> <power /> <apply> <plus /> <ci> y </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> x </ci> <cn type='integer'> 4 </cn> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <power /> <ci> y </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <ci> x </ci> <cn type='integer'> 2 </cn> 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Rule Form





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





2007-05-02





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