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

• To: mathgroup at smc.vnet.net
• 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
>