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Math Help - Solving trigonometry/algebra equation

  1. #1
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    Combined trigonometry/exponential equation

    Hi, I'm trying to solve the following to find the angle (Beta).

    -----------------------------------
    Sin(Alfa)= Cos(Beta) * e^(tan(Beta)*(pi/6 - Alfa +Beta))

    Where Alfa = 1.2566 rad


    --------------------------------------

    The correct answer for Beta should be 0.0611 rad. Could anyone provide steps to obtain this answer.
    Last edited by rashmil; September 22nd 2013 at 06:17 PM.
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  2. #2
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    Re: Solving trigonometry/algebra equation

    Hey rashmil.

    You may have to use a numerical solver for this problem, but never the less you need all beta terms on one side and everything else on the other.

    Hint: Use e^(a+b) = e^a * e^b and get everything in terms of Beta on LHS (You will have a cos term and an exponential term that are functions of beta).

    If you need to use a numerical solver, then something like MATLAB (or Octave) should suffice. You could also R as well which is free (as is Octave).
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  3. #3
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    Re: Combined trigonometry/exponential equation

    Quote Originally Posted by rashmil View Post
    Hi, I'm trying to solve the following to find the angle (Beta).

    -----------------------------------
    Sin(Alfa)= Cos(Beta) * e^(tan(Beta)*(pi/6 - Alfa +Beta))

    Where Alfa = 1.2566 rad
    --------------------------------------

    The correct answer for Beta should be 0.0611 rad. Could anyone provide steps to obtain this answer.
    consider this:
    Solving trigonometry/algebra equation-untitled2.gif
    Thanks from topsquark
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  4. #4
    Forum Admin topsquark's Avatar
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    Re: Combined trigonometry/exponential equation

    Just to give you a hint (it may help you find a solution method) there is only one solution in the interval  \[ - \pi , \pi \] .

    -Dan
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