trigonometry - Solve simple trig equation

I would like to solve this equation:

$$-x\sin(x)=\cos(x)$$

But Solve in Mathematica doesn't work:

This system cannot be solved with the methods available to Solve

Being a beginner, I don't know any other ways to solve this equation. Any suggestions?

Thanks!

Answer

Restrict the domain:

Solve[-x Sin[x]==Cos[x]&&-30<=x<=30,x,Reals]//N

{{x->-28.2389},{x->-25.0929},{x->-21.9456},{x->-18.7964},{x->-15.6441},{x->-12.4865},{x->-9.31787},{x->-6.12125},{x->-2.79839},{x->2.79839},{x->6.12125},{x->9.31787},{x->12.4865},{x->15.6441},{x->18.7964},{x->21.9456},{x->25.0929},{x->28.2389}}

Comments

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