Most studies on low-frequency electromagnetic cyclotron waves have assumed a small wave amplitude, which ensures the reasonable application of linear and quasi-linear theories. However, the topic of large-amplitude electromagnetic cyclotron waves has not received much attention. Using Magnetospheric Multiscale measurements, this study observes low-frequency, left-hand circularly polarized electromagnetic waves with magnetic fluctuation similar to 1-2 nT in the dusk flank side of the Earth's magnetosheath. Considering the ambient magnetic field similar to 15 nT therein, the relative wave amplitude is of the order of 0.1. These large magnetic field fluctuations result in a periodic variation of the ion pitch angle. The electron pitch angle exhibits a localized distribution feature with a timescale approximating the wave period. Moreover, some electrons are trapped at a pitch angle similar to 90 degrees, and the trapping is more remarkable as strong waves arise. These two features of the electron pitch angle distribution imply that the trapping of electrons (partly) results from large-amplitude electromagnetic cyclotron fluctuations. Our results illustrate the important role of large-amplitude electromagnetic cyclotron waves on the dynamics of charged particles.