Floating offshore wind turbines are subjected to platform motions that modify the local velocity experienced by the rotor. This work analyzes how variations in the platform motions affect the aerodynamic power of a floating wind turbine. Idealized wind conditions and rigid wind turbine are considered. The platform motions are prescribed by the user and the coupled motions considered are pitch-surge, pitch-yaw and surge-yaw. The main novelties of the work consist in the fact that multiple motions are prescribed simultaneously, including yaw, and that the prescribed motions present a difference in phase. In absence of wind turbine controller, the pitch-surge coupling shows significant increase in average power production with respect to fixed conditions when either the amplitude or frequency are increased. This gain is maximum when surge and pitch are in phase, and is almost zero in phase opposition. The presence of the controller reverses the behavior and introduces a loss in average power along with increasing amplitudes. Phase shift analysis is particularly interesting in the surge and pitch cases: the controller introduces an upper limit in power, and phase opposition is now desirable. The yaw degree of freedom is shown to be of secondary importance in every condition.