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ArcCos






Mathematica Notation

Traditional Notation









Elementary Functions > ArcCos[z] > Transformations > Related transformations > Differences involving the direct function > Involving tan-1(z)





http://functions.wolfram.com/01.13.16.0171.01









  


  










Input Form





ArcCos[x] - ArcTan[y] == Pi/2 - ((x + Sqrt[1 - x^2] y) (Pi - 2 ArcSin[(Sqrt[1 - x^2] - x y)/Sqrt[1 + y^2]]) + 2 Pi (x + Sqrt[1 - x^2] y + Sqrt[1 + y^2] Sqrt[(x^2 + 2 x Sqrt[1 - x^2] y + y^2 - x^2 y^2)/(1 + y^2)]) Floor[(Arg[I x + Sqrt[1 - x^2]] + Arg[(I - y)/Sqrt[1 + y^2]])/(2 Pi)] - 2 Pi (-x - Sqrt[1 - x^2] y + Sqrt[1 + y^2] Sqrt[(x^2 + 2 x Sqrt[1 - x^2] y + y^2 - x^2 y^2)/(1 + y^2)]) Floor[-((-Pi + Arg[I x + Sqrt[1 - x^2]] + Arg[(I - y)/Sqrt[1 + y^2]])/ (2 Pi))])/(2 Sqrt[(x + Sqrt[1 - x^2] y)^2/(1 + y^2)] Sqrt[1 + y^2])










Standard Form





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MathML Form







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</apply> <apply> <arg /> <apply> <times /> <apply> <plus /> <imaginaryi /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> y </ci> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> y </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <pi /> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02





© 1998- Wolfram Research, Inc.