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Re: How can I solve this equation with Solve or Reduce or whatever for

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  • Subject: [mg128561] Re: How can I solve this equation with Solve or Reduce or whatever for
  • From: Bill Rowe <readnews at sbcglobal.net>
  • Date: Sun, 4 Nov 2012 00:43:41 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • Delivered-to: l-mathgroup@wolfram.com
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On 11/2/12 at 12:42 AM, lrebanks at gmail.com (Lea Rebanks) wrote:

>Given that the following equation is true.

>Clear[NoOf360Rotations]

>NoOf360Rotations = 108

>ArcTan[Tan[Degree*(180 - 1.5267134447254718*(18.43494882292201 +
>360*NoOf360Rotations))]] == 0.23101849674392247

>TRUE

>How can I solve this equation with Solve or Reduce or whatever for
>the required value NoOf360Rotations = 108

>Only want Integer return of NoOf360Rotations AND to equal 108

Even though Mathematica indicates your equation is true when the
number of rotations is 108, there really isn't a way to have
Mathematica return 108 without you providing more information.
The problem is there are an infinite number of solutions to your
equation. If you do

Plot[ArcTan[
    Tan[Degree*(180 -
        1.5267134447254718*(18.43494882292201 +
           360*NoOf360Rotations))]] -
   0.23101849674392247, {NoOf360Rotations, 106, 110}]

you will see several zero crossings, each is a separate solution
to your equation. While it is true in this restricted range 108
appears to be the only integral solution, it is undoubtedly true
there are other integral solutions. Further, you make the
problem even more difficult by asking for an integer when you
have inputed machine precision values.




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