The dynamic phase transitions have been studied, within a mean-field approach, in the kinetic spin-1 Ising model Hamiltonian with arbitrary bilinear and biquadratic pair interactions in the presence of a time varying (sinusoidal) magnetic field by using the Glauber-type stochastic dynamics. The nature (first- or second-order) of the transition is characterized by investigating the behavior of the thermal variation of the dynamic order parameters. The dynamic phase transitions (DPTs) are obtained and the phase diagrams are constructed in the temperature and magnetic field amplitude plane and found six fundamental types of phase diagrams. Phase diagrams exhibit one or two dynamic tricritical points depending on the biquadratic interaction (K). Besides the disordered (D) and ferromagnetic (F) phases, the FQ + D, F + FQ and F + D coexistence phase regions also exist in the system and the F and F + D phases disappear for high values of K.