wolfram-mathematicatrigonometryequationmathematica-8

Solving an equation in terms of unknown constants wolfram mathematica

I want to solve the following equation. I want to get an expression of x in terms of unknown constants alpha and beta. Does anyone know how to solve this in Matlab or Mathematica? Thanks.

Here's my one line code in wolfram Mathematica. 

'Assuming[alpha>beta>0,Solve[Cos(alpha*Cos(x)) + Cos(beta*Cos(x)) -1.96 ==0,x]] '
Solution

  • Since it doesn't appear simple to get an analytic solution, perhaps a graphic showing the behavior might provide some insight about what to do next.

    ListPointPlot3D[Reap[Do[
   {alpha, beta, x} = RandomReal[{0, 2 Pi}, 3];
   If[alpha > beta,
      err = Norm[Cos[alpha*Cos[x]]+Cos[beta*Cos[x]]-1.96];
      If[err < .01, Sow[{alpha, beta, x}]]
],{10^6}]][[2, 1]], ViewPoint->{0, -2., 0}]

    enter image description here

    Once that displays on your monitor you can either adjust the numbers inside that Viewpoint or you might be able to place your mouse inside the graphic, press and hold the left mouse button and drag to rotate the image around.

    That graphic seems to show that the solutions lie within a fairly well defined region.

    Once you have looked at this then you might bump the range of the random numbers up to {0,4Pi} because it looks like there is more interesting behavior for larger values of alpha and beta.