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

*To*: mathgroup at smc.vnet.net*Subject*: [mg39657] Re: [mg39620] Domain of Sin[ArcSin[x]] ?*From*: Dr Bob <drbob at bigfoot.com>*Date*: Thu, 27 Feb 2003 00:33:59 -0500 (EST)*References*: <200302260742.CAA18970@smc.vnet.net>*Reply-to*: drbob at bigfoot.com*Sender*: owner-wri-mathgroup at wolfram.com

If you don't want to choose the proper limits for the plot, YOU have to decide what you want plotted when ArcSin@x isn't real. For instance, Plot[Sin@Re@ArcSin@x, {x, -2, 2}] or Plot[Switch[Im@ArcSin@x, 0, x, _, 0], {x, -2, 2}] or Plot[Sin@Re@ArcSin@x, {x, -1, 1}] Your choice. Alternatively, just Plot the Sin function and say, "See, the values are all between -1 and 1, so that's the domain of ArcSin. The range of the function is the (largest possible) domain of the inverse." Bobby On Wed, 26 Feb 2003 02:42:54 -0500 (EST), Michael Buescher <mbuescher at hb.edu> 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 > > > -- majort at cox-internet.com Bobby R. Treat

**References**:**Domain of Sin[ArcSin[x]] ?***From:*mbuescher@hb.edu (Michael Buescher)