Recently, Shi et al. [2008 Phys. Lett. A 372 5922] have studied the dynamical response of the kinetic Ising model in the presence of a sinusoidal oscillating field and presented the dynamic phase diagrams by using an effective-field theory (EFT) and a mean-field theory (MFT). The MFT results are in conflict with those of the earlier work of Tome and de Oliveira, [1990 Phys. Rev. A 4 1 4251]. We calculate the dynamic phase diagrams and find that our results are similar to those of the earlier work of Tome and de Oliveira; hence the dynamic phase diagrams calculated by Shi et a l. are incomplete within both theories, except the low values of frequencies for the MFT calculation. We also investigate the influence of external field frequency (omega) and static external field amplitude (h(0)) for both MFT and EFT calculations. We find that the behaviour of the system strongly depends on the values of omega and h(0).