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

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  • Subject: [mg39639] Re: [mg39620] Domain of Sin[ArcSin[x]] ?
  • From: Andrzej Kozlowski <akoz at>
  • Date: Thu, 27 Feb 2003 00:27:34 -0500 (EST)
  • Sender: owner-wri-mathgroup at

What would you like to happen when ArcSin[x] is not a real number? If 
you are happy with the usual error messages ("not a machine size real 
...") then you can do something like this:


IsReal[x_] := If[Element[x, Reals], x]

and evaluate

Plot[Sin[IsReal[ArcSin[x]]], {x, -3, 3}]

Andrzej Kozlowski
Yokohama, Japan

On Wednesday, February 26, 2003, at 04:42  pm, 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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