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))

Where Alfa = 1.2566 rad

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The correct answer for Beta should be 0.0611 rad. Could anyone provide steps to obtain this answer.

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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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))

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:

Attachment 29251

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 $\displaystyle \[ - \pi , \pi \] $.

-Dan