Abstract: The periodic potentials have been widely applied in the fields of engineering, physics, chemistry and neurobiology, whose stochastic dynamics has become the focus of nonlinear science. Trichotomous noise is a kind of three-level Markovian noise and can converge to dichotomous noise or Gaussian white noise under some limits. The trichotomous noise is a better representation of real noise than the widely used Gaussian white noise to display the diversity of environmental excitation. This paper studies the evolutions of probability density function (PDF) and stochastic resonance (SR) in a periodic potential driven by additive and multiplicative trichotomous noise. The average stationary joint PDF and transient joint PDF are obtained by numerical simulation. It is found that the shape of the stationary PDF has the multi-modal structure as the amplitude of the periodic force increases, which indicates the noise-induced hopping among the potential wells. Furthermore, the stochastic energy method is used to explore the SR phenomenon. The obtained results show that the average input energy curve attains a maximum at an optimal noise intensity and amplitude of periodic force. That is, the SR happens. Moreover, the SR happens at an optimal transition rate of noise and the proper amplitude of periodic force under the excitation of only multiplicative or additive noise. Especially, for the case of additive noise, transition rate of additive noise can induce the suppression of SR for a small amplitude of periodic force. While the SR appears at a proper transition rate of additive noise for a large amplitude of periodic force.