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
>
>
>
>