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

*To*: mathgroup at smc.vnet.net*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*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net

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.