[Date Index]
[Thread Index]
[Author Index]
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)
Prev by Date:
**Re: Eliminate Complex Roots**
Next by Date:
**Re: Re: How to do a SQL type operation???**
Previous by thread:
**Re: Solve or Reduce?**
Next by thread:
**Re: Re: Re: Solve or Reduce?**
| |