# Solving trigonometry/algebra equation

• Sep 22nd 2013, 06:09 PM
rashmil
Combined trigonometry/exponential equation
Hi, I'm trying to solve the following to find the angle (Beta).

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

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The correct answer for Beta should be 0.0611 rad. Could anyone provide steps to obtain this answer.
• Sep 22nd 2013, 07:06 PM
chiro
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).
• Sep 22nd 2013, 11:16 PM
votan
Re: Combined trigonometry/exponential equation
Quote:

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

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

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