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

*To*: mathgroup at smc.vnet.net*Subject*: [mg39639] Re: [mg39620] Domain of Sin[ArcSin[x]] ?*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Thu, 27 Feb 2003 00:27:34 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

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: define IsReal[x_] := If[Element[x, Reals], x] and evaluate Plot[Sin[IsReal[ArcSin[x]]], {x, -3, 3}] Andrzej Kozlowski Yokohama, Japan http://www.mimuw.edu.pl/~akoz/ http://platon.c.u-tokyo.ac.jp/andrzej/ 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 > > > >