We have investigated the effect of nucleon and delta resonances with spins , , and in the kaon photoproduction process by using two covariant isobar models. The formalism for high-spin propagators and interaction Lagrangians were adopted from the works of Pascalutsa and Vrancx et al. The calculated scattering amplitudes were decomposed into six Lorentz- and gauge-invariant matrices, from which we calculated the cross sections and polarization observables. The unknown parameters in the amplitudes, i.e., the coupling constants and hadronic form factor cutoffs, were obtained by fitting the calculated observables to experimental data. In the channels the inclusion of and resonances improves the agreement between model calculations and experimental data significantly and reduces the dominance of resonances in the model by increasing the hadronic form factor cutoff of the Born terms. Furthermore, the inclusion of these resonances reduces the number of resonance structures in cross sections, including the structure in the differential cross section at , which could become a hint of the narrow resonance. In the channels the inclusion of , , , , and states also significantly improves the model and increases the hadronic form factor cutoff of the Born terms. However, different from the channels, the inclusion of these high-spin resonances leads to more resonance structures in the differential cross section. This investigation reveals that the second and third peaks in the differential cross section originate from the and resonances, respectively. We have also evaluated the resonance properties at the pole positions and using the Breit-Wigner method. In both and channels the inclusion of the high-spin baryon resonances was found to improve the agreement between the resonance properties obtained in this study and those listed by the Particle Data Group.