Although some plasma waves exhibit the largest growth rate and amplitude at 90deg wave normal angle (WNA), particle scattering by these waves in a quasilinear (QL) sense has not been examined previously. Using test-particle calculation and QL theory, the present study investigates the proton scattering by equatorial fast magnetosonic waves (MSWs; a.k.a equatorial noise) with varying WNAs including 90deg. Comparison with the diffusion coefficients in momentum space obtained from the test-particle approach indicates that the QL diffusion coefficients given by, e.g., Kennel and Engelmann (1966) are valid up to 90deg WNA, provided that MSWs described conform to the usual QL theory assumptions. The test-particle dynamics due to MSWs at 90deg WNA are examined in detail. Although in the QL picture, protons are only supposed to resonate with MSWs of integer harmonic frequencies at perpendicular propagation, the presence of slightly off-integer harmonic modes as part of a narrowband discrete spectrum of incoherent MSWs plays an important role in making the proton scattering stochastic. Considering the recent test-particle result of bounce-averaged resonance of energetic protons, non-zero wave power at the WNAs >~ 89.5deg typically excluded in QL diffusion can be important for ring current proton dynamics.