  We have investigated the effect of nucleon and delta resonances with spins
11/2, 13/2, and 15/2 in the kaon photoproduction process $\gamma + N \to K + Y$
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 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 $K\Lambda$ channels the
inclusion of $N(2600)I_{1,11}$ and $N(2700)K_{1,13}$ 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 $K^0\Lambda$ differential cross section at
$W\approx 1650$ MeV, which could become a hint of the narrow resonance. In the
$K\Sigma$ channels the inclusion of $N(2600)I_{1,11}$, $N(2700)K_{1,13}$,
$\Delta(2420)H_{3,11}$, $\Delta(2750)I_{3,13}$, and $\Delta(2950)K_{3,15}$
states also significantly improves the model and increases the hadronic form
factor cutoff of the Born terms. However, different from the $K\Lambda$
channels, the inclusion of these high-spin resonances leads to more resonance
structures in the $K^+\Sigma^0$ differential cross section. This investigation
reveals that the second and third peaks in the $K^+\Sigma^0$ differential cross
section originate from the $\Delta(2000)F_{35}$ and $N(2290)G_{19}$ resonances,
respectively. We have also evaluated the resonance properties at the pole
positions and using the Breit-Wigner method.
