  We have performed high precision experimental measurements of spin precession
using a dressed $^3$He atomic beam. Spin-dressing uses an oscillating magnetic
field detuned to high frequency which is orthogonal to a static magnetic field
to effectively change the gyromagnetic ratio of a spin. We verify the validity
of the spin-dressing Hamiltonian in regions beyond the limiting solution in
which the Larmor frequency is much smaller than the frequency of the dressing
field. We also evaluate the effect of magnetic field misalignment, e.g. if the
oscillating magnetic field is not orthogonal to the static magnetic field.
Modulation of the dressing field parameters is also discussed, with a focus on
whether such a modulation can be approximated merely as a time dependent,
dressed gyromagnetic ratio. Furthermore, we discuss implications for a proposed
search for the neutron electric dipole moment, which would employ spin-dressing
to make the effective $^3$He and neutron magnetic moments equal.
