Re: Domain of Sin[ArcSin[x]] ?
- To: mathgroup at smc.vnet.net
- Subject: [mg39637] Re: Domain of Sin[ArcSin[x]] ?
- From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
- Date: Thu, 27 Feb 2003 00:27:24 -0500 (EST)
- Organization: Universitaet Leipzig
- References: <b3hs25$ik5$1@smc.vnet.net>
- Reply-to: kuska at informatik.uni-leipzig.de
- Sender: owner-wri-mathgroup at wolfram.com
Hi,
Plot[(y = ArcSin[x]; If[Head[y] === Complex, 0, Sin[y]]), {x, -2, 2}]
Regards
Jens
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