  Gravitational waves from a binary with a single dynamically significant spin,
notably including precessing black hole-neutron star (BH-NS) binaries, let us
constrain that binary's properties: the two masses and the dominant black hole
spin. Based on a straightforward fourier transform of $h(t)$ enabled by the
corotating frame, we show the Fisher matrix for precessing binaries can be
well-approximated by an extremely simple semianalytic approximation. This
approximation can be easily understood as a weighted average of independent
information channels, each associated with one gravitational wave harmonic.
Generalizing previous studies of nonprecessing binaries to include critical
symmetry-breaking precession effects required to understand plausible
astrophysical sources, our ansatz can be applied to address how well
gravitational wave measurements can address a wide range of astrophysical and
fundamental questions. Our approach provides a simple method to assess what
parameters gravitational wave detectors can measure, how well, and why.
