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

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  • Subject: [mg128562] Re: How can I solve this equation with Solve or Reduce or whatever for
  • From: Dana DeLouis <dana01 at me.com>
  • Date: Sun, 4 Nov 2012 00:44:01 -0400 (EDT)
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> ArcTan[Tan[Degree*(180 - 1.5267134447254718*(18.43494882292201 +
> 360*NoOf360Rotations))]] == 0.23101849674392247

> Only want Integer return of NoOf360Rotations AND to equal 108


Hi.  Another way might be to move everything to the left-hand side of the equation.


ArcTan[Tan[Degree*(180-1.5267134447254718*(18.43494882292201+360*x))]] - 0.23101849674392247

f=FullSimplify[%]

-0.231018+ArcTan[Tan[2.65037 -9.59262 x]]

Now:

Minimize[{Abs[f],0<x<200},x,Integers]

{2.77556*10^-17,{x->108}}


The value of 2.77*10^-17  is pretty close to zero, and will trigger True if compared at machine precision.

Here's another idea if another problem in the future was not as close to zero.


Table[ f->x,  {x,105,110}]

{0.503537->105,
0.335691->106,
0.167846->107,
2.77556*10^-17->108,
-0.167846->109,
-0.335691->110}


Nearest[%,0]
{108}

= = = = = = = = = =
HTH  :>)
Dana DeLouis
Mac & Mathematica 8
= = = = = = = = = =




On Friday, November 2, 2012 1:13:06 AM UTC-4, Lea Rebanks wrote:
> Hi All,
> 
> 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
> 
> Any help or advice gratefully received.
> 
> Best regards,
> Lea=85




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