I'm trying to find some angles for my characteristic equation , I need to know the roots or possible answers to cosine equation
$$1-\cos(u)\cdot\cosh(w)=0,$$
and
$$u=\sqrt{\lambda_1}\cdot L.$$
$$w=\sqrt{\lambda_2}\cdot L.$$
What are the general possible values (angles) for parameters $u$ and $w$ in pairs? I need for different modes in general (mode 1,2,3,...)
Thank you very much.