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