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

*To*: mathgroup at smc.vnet.net*Subject*: [mg39648] RE: [mg39620] Domain of Sin[ArcSin[x]] ?*From*: "David Park" <djmp at earthlink.net>*Date*: Thu, 27 Feb 2003 00:29:18 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Michael, I think that Sin is an analytic function and it's inverse ArcSin is also, except perhaps at singular points. So ArcSin[x] is defined for real x outside of -1 < x < 1. But you could try something like this to eliminate points where ArcSin[x] is complex. f[x_] := With[{as = ArcSin[x]}, If[FreeQ[as, Complex], Sin[as], 0]] Plot[f[x], {x, -2, 2}]; David Park djmp at earthlink.net http://home.earthlink.net/~djmp/ From: Michael Buescher [mailto:mbuescher at hb.edu] To: mathgroup at smc.vnet.net 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