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