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)
- Domain of Sin[ArcSin[x]] ?