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Domain of Sin[ArcSin[x]] ?

  • To: mathgroup at
  • Subject: [mg39620] Domain of Sin[ArcSin[x]] ?
  • From: mbuescher at (Michael Buescher)
  • Date: Wed, 26 Feb 2003 02:42:54 -0500 (EST)
  • Organization: Hathaway Brown School
  • Sender: owner-wri-mathgroup at

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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