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ArcCos






Mathematica Notation

Traditional Notation









Elementary Functions > ArcCos[z] > Transformations > Related transformations > Linear combinations involving the direct function > Involving sin-1(z)





http://functions.wolfram.com/01.13.16.0204.01









  


  










Input Form





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










Standard Form





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MathML Form







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Rule Form





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





2007-05-02