Solve Trigonometric Equation

Can anyone help solve the below for 'a'


I've reduced it to



Which I think is right, but I can't get any further without just ending up with different forms that appear more complex.

Tom Mattson

Staff Emeritus
Science Advisor
Gold Member
What makes this equation tough is the fact that you've got 2 different trig functions running around there. What's more you've got 2 different arguments in your cosine functions. I would try to express everything in terms of [itex]\cos(a)[/itex], so that you end up with a polynomial equation in that quantity.

Try to make use of the following identities:



I don't think you're going to get a closed form expression for a, but if you have numerical values for the parameters you will be able to get approximate solutions.

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