This paper introduces a rigorous derivation of the quasi-geostrophic (QG) equations of large scale ocean as the Rossby number goes to zero. We follow classical techniques for the derivation (as in [BB94]), but the primitive equations that we consider account for all the rotating terms, as in [LPR10]. We end up with a slightly different QG model with a tilted vertical direction, which has been illustrated in previous works (see [SHE04, WB06, GZMvH08]).