# 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]==0I usually use Solve for polynomial equations, but neither Solve not Reduce can face these kind of problems Can someone please help me?Thank You
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Posted 2 months ago
 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. Attachments: