  The azimuthal single target-spin asymmetries for pi^{+} production in
semi-inclusive deep inelastic scattering of leptons off longitudinally
polarized protons are evaluated using two main approaches available in the
literature. It is shown that the approximation where the twist-2 transverse
quark spin distribution in the longitudinally polarized nucleon is small enough
to be neglected leads to a consistent description of all existing asymmetries
observed by the HERMES experiment.
