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MathGroup Archive 2006

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Re: Re: Solve or Reduce?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg64412] Re: [mg64398] Re: Solve or Reduce?
  • From: Math Novice <math_novice_2 at yahoo.com>
  • Date: Thu, 16 Feb 2006 03:05:20 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

  I am trying to find the angle b corresponding to the points on the circumference of the circle (5+8 Cos[b], 7+8 Sin[b]) that are a distance of 7 units from a point on the circumference of the circle (13 cos[a], 13 Sin[a]) for angles a in the first quadrant. (5+8 Cos[b], 7+8 Sin[b]) is a circle of radius 8 and center (5,7) and (13 cos[a], 13Sin[a]) is a circle of radius 13 and center (0,0). 
   
  (13,0) on the circle (13 cos[a], 13 Sin[a]) and (13,7) on (5+8 Cos[b], 7+8 Sin[b]) are the first set of points that are 7 units apart when the angle a (of the larger circle ) is equal to 0. As I increase the value of a and use my compass (set at 7 units) to measure on the printout of the diagram of the two circles it seems that there should always be an angle for b that corresponds to a and b should always increase as a increases but something happens at about 32 degrees. For some calculations b starts to decrease as a increases past 32 degrees or with some other calculations b becomes negative as a increases past 32 degrees. Any idea of what I?m going wrong?
   
  

Renan <renan.birck at gmail.com> wrote:
  Math Novice, in comp.soft-sys.math.mathematica:
> 
> I'm looking to solve the equation 
> 
> (13 Cos[q]-(5+8 Cos[f]))^2+(13 Sin[q]-(7+8 Sin[f]))^2?49
> 
> so that I can graph phi as a function of theta in the first quadrant only. 
> A graph of the solution obtained using the Solve command produces unexpected results and
> I haven't used Mathematica much so I'm having trouble intrepreting the results that the 
> Reduce operation produces. 
> I understand that the solution is periodic but 
> can someone interpret what the other symbols in the solution mean, e.g., C[1], &&, || etc.?

C[1], C[2], ... C[n] = arbitrary constant
&& = "And" operator (e.g. True && False == False, True && True == True)
|| = "Or" operator (e.g. False || True == True, False || False == True)


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