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Re: Solving a simple equation

  • To: mathgroup at smc.vnet.net
  • Subject: [mg121874] Re: Solving a simple equation
  • From: dimitris <dimmechan at yahoo.com>
  • Date: Wed, 5 Oct 2011 04:03:52 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <j6e675$kds$1@smc.vnet.net>

Hi.
1) You haven't specified value for ma1.
2) I guess that with degree you meen Degree.
3) You specified value for Capital Theta instead of Theta.
4) The equation has infinity roots as it is a Transcendental equation.
Use FindRoot instead of NSolve. Be careful with the singularities at
n*Pi, n integer.

\[Kappa] = 1.4;
\[Theta] = 10.;
ma1 = 5.;

eq = Tan[\[Theta]*Degree] - ( 2*Cot[\[Beta]]*((ma1^2*Sin[\[Beta]]^2 -
1)/(ma1^2*(\[Kappa] + Cos[2*\[Beta]]) + 2)));

pl = Plot[eq, {\[Beta], -11, 11}, Exclusions -> Table[n Pi, {n, -3,
3}], Frame -> True, Axes -> {True, False}]

For example

FindRoot[eq == 0, {\[Beta], 1}]
FindRoot[eq == 0, {\[Beta], 1.5}]
{\[Beta] -> 0.338175}
{\[Beta] -> 1.52629}

5) Another way is using Reduce.

Clear["Global*`"]

\[Kappa] = 14/10;
\[Theta] = 10;
ma1 = 5;
eq = Tan[\[Theta]*Degree] - (  2*Cot[\[Beta]]*((ma1^2*Sin[\[Beta]]^2 -
1)/(ma1^2*(\[Kappa] + Cos[2*\[Beta]]) + 2)));

 Reduce[eq == 0, \[Beta]]
(*output ommited*)


Regards
Dimitris



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