  Extreme mass ratio inspirals (EMRIs) will be important sources for future
space-based gravitational-wave detectors. In recent work, tidal resonances in
binary orbital evolution induced by the tidal field of nearby stars or black
holes have been identified as being potentially significant in the context of
extreme mass-ratio inspirals. These resonances occur when the three orbital
frequencies describing the orbit are commensurate. During the resonance, the
orbital parameters of the small body experience a jump leading to a shift in
the phase of the gravitational waveform. In this paper, we treat the tidal
perturber as stationary and restricted to the equatorial plane, and present a
first study of how common and important such resonances are over the entire
orbital parameter space. We find that a large proportion of inspirals encounter
a low-order resonance in the observationally important regime. While the
instantaneous effect of a tidal resonance is small, its effect on the
accumulated phase of the gravitational waveform of an EMRI system can be
significant due to its many cycles in band; we estimate that the effect is
detectable for a significant fraction of sources. We also provide fitting
formulae for the induced change in the constants of motion of the orbit due to
the tidal resonance for several low-order resonances.
