  We discuss a generalised version of Sklyanin's Boundary Quantum Inverse
Scattering Method applied to the spin-1/2, trigonometric sl(2) case, for which
both the twisted-periodic and boundary constructions are obtained as limiting
cases. We then investigate the quasi-classical limit of this approach leading
to a set of mutually commuting conserved operators which we refer to as the
trigonometric, spin-1/2 Richardson-Gaudin system. We prove that the rational
limit of the set of conserved operators for the trigonometric system is
equivalent, through a change of variables, rescaling, and a basis
transformation, to the original set of trigonometric conserved operators.
Moreover we prove that the twisted-periodic and boundary constructions are
equivalent in the trigonometric case, but not in the rational limit.
