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Re: Domain of Sin[ArcSin[x]] ?

  • To: mathgroup at
  • Subject: [mg39637] Re: Domain of Sin[ArcSin[x]] ?
  • From: Jens-Peer Kuska <kuska at>
  • Date: Thu, 27 Feb 2003 00:27:24 -0500 (EST)
  • Organization: Universitaet Leipzig
  • References: <b3hs25$ik5$>
  • Reply-to: kuska at
  • Sender: owner-wri-mathgroup at


Plot[(y = ArcSin[x]; If[Head[y] === Complex, 0, Sin[y]]), {x, -2, 2}]


Michael Buescher wrote:
> I want to demonstrate to my students that in the real number system,
> Sin[ArcSin[x]] is only defined on [-1,1] because that is the domain of
> ArcSin[x].  When I Plot the composition, however, I get Sin[ArcSin[x]] =
> x for all real numbers, not just on [-1,1].  I tried this both with and
> without the RealOnly package.
> Is there any way to ensure that Mathematica uses only real numbers in
> its calculations, so that Sin[ArcSin[x]] is undefined when ArcSin[x] is
> not a real number?
> Michael Buescher
> Hathaway Brown School

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