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x-ArcSin[Sin[x]]

• To: mathgroup at smc.vnet.net
• Subject: [mg50007] x-ArcSin[Sin[x]]
• From: Paul Muller <paul.muller-at-epfl.ch at sicinfo2.epfl.ch>
• Date: Wed, 11 Aug 2004 05:53:03 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

Dear all,

I know this question was already discussed in 1995 (that's what I found in Google), but 
I would like to know if anything has been changed in the Mathematica implementation of 
ArcSin[Sin[x]].

http://groups.google.ch/groups?q=Mathematica+%2BArcSin%5BSin&hl=de&lr=&ie=UTF-8&selm=DDwG4y.GrJ%40wri.com&rnum=1

I am calculating the magnetic field in any point of the plane of a spire (or spiral 
inductor). When I apply this to the center of the spire, I get the following integral:

Integrate[Sin[x+ArcSin[Sin[Pi/2-x]]], {x, 0, 2Pi}]

According to textbook results for magnetic fields, the result should be 2Pi. Because of 
the definition of ArcSin[Sin[x]] in Mathematica, the integral results in Pi.
Maybe I'm not careful enough when using the ArcSin function on the angles of
my geometric problem (I'm an engineer, not a mathematician), but it would
be helpful if this integral was solved "correctly".

Any updates on this are welcome.

Thanks in advance

Paul Muller

• Follow-Ups:
  • Re: x-ArcSin[Sin[x]]
    • From: DrBob <drbob@bigfoot.com>