  Pion elastic, charge exchange scattering and induced eta production on the
trinucleon systems are investigated in a coupled-channels approach in momentum
space with Fadeev wave functions. The channel $\pi N \rightarrow \eta N$ is
included using an isobar model with S-, P-, and D-wave resonances. While the
coherent reactions like $^3$He($\pi,\pi)^3$He can be reasonably well reproduced
up to $T_{\pi}$=500 MeV, large discrepancies appear for the incoherent
processes, $^3$He($\pi^-,\pi^0)^3$H and $^3$He($\pi^-,\eta)^3$H at backward
angles and energies above $\Delta$-resonance. In the forward direction the
$(\pi,\eta)$ calculations underestimate the experimental measurements very
close to threshold but agreement with the data improves with increasing pion
energy. Predictions are made for the asymmetries of the various reactions on
polarized $^3$He.
