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MathGroup Archive 2003

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

  • To: mathgroup at smc.vnet.net
  • Subject: [mg39641] Re: [mg39620] Domain of Sin[ArcSin[x]] ?
  • From: Sseziwa Mukasa <mukasa at jeol.com>
  • Date: Thu, 27 Feb 2003 00:27:46 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

On Wednesday, February 26, 2003, at 02:42 AM, 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
>

One possibility is to make your own ArcSin that is only valid on the 
interval [-1,1].

Regards,

Ssezi



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