  We present a measurement of the spin-dependent cross sections for the
\vec{^3He}(\vec{e},e')X} reaction in the quasielastic and resonance regions at
four-momentum transfer 0.1 < Q^2< 0.9 GeV^2. The spin-structure functions have
been extracted and used to evaluate the nuclear Burkhardt--Cottingham and
extended GDH sum rules for the first time. Impulse approximation and exact
three-body Faddeev calculations are also compared to the data in the
quasielastic region.
