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Solve trig equations with unknowns both in and out trig functions?

Posted 2 months ago
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Good morning everyone,

I'm new to the forum and a Wolfram beginner. I'm having troubles calculating trigonometric functions with unknowns both in and out of the brackets of trigonometric functions

eg: Cos[x] - x Sin[x]==0

I usually use Solve for polynomial equations, but neither Solve not Reduce can face these kind of problems enter image description here

Can someone please help me?

Thank You

3 Replies

Try restricting the range of the variable:

Solve[Cos[x] - x*Sin[x] == 0 && Abs[x] < 10, x]

A little more than the problem you are trying to solve:

If you follow the SE article carefully, you will have a very nice conclusion (though you have Cotc, the argument is the same)

Therefore, you have a numerically robust way to find nth solution when n is very large:

In[1]:= n=100;
In[2]:= FindRoot[Cot[x]==x,{x,n*\[Pi]+1/(n*\[Pi])}]
Out[2]= {x->314.162}

A notebooks is attached for you to play around.

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Posted 2 months ago

Thank you very much to both of you for your answers, they will be precious.

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