Motivated by the recent experimental observation of quantum oscillations in the underdoped cuprates, we study the cyclotron and infrared Hall effective masses in an anisotropic Fermi liquid characterized by an angle-dependent quasiparticle residue Z(q). Our primary motivation is to explain the relatively large value of the cyclotron mass observed experimentally and its relation with the effective Hall mass. Using a phenomenological model of an anisotropic Fermi liquid, we find that the cyclotron mass is enhanced by a factor < 1/Z(q)>, while the effective Hall mass is proportional to < Z(q)>/< Z(q)(2)>, where <(...)> implies an averaging over the Fermi surface. If the Z-factor becomes small in some part of the Fermi surface ( e. g., in the case of a Fermi arc), the cyclotron mass is enhanced sharply while the infrared Hall mass may remain small.