How can I find the frequency from the lagrangian of a small oscillation?

The lagrangian is L = m/2 dx/dt + sinx

When I put this in the EL I get

d^2x/dt^2 + cosx = 0

I don't know what to do after this point to find X.

Should I do an taylor expansion on cosx and approximate it to cosx = 1 - x^2/2 since it is a small oscillation? I still can't solve this DE though, my math knowledge is not sufficient.