  We have measured the projected rotational velocities (vsini) in a number of
symbiotic stars and M giants using high resolution spectroscopic observations.
On the basis of our measurements and data from the literature, we compare the
rotation of mass-donors in symbiotics with vsini of field giants and find that:
  (1) the K giants in S-type symbiotics rotate at vsini>4.5 km/s, which is 2-4
times faster than the field K giants;
  (2) the M giants in S-type symbiotics rotate on average 1.5 times faster than
the field M giants. Statistical tests show that these differences are highly
significant: p-value < 0.001 in the spectral type bins K2III-K5III,
M0III-M6III, and M2III-M5III;
  (3) our new observations of D'-type symbiotics also confirm that they are
fast rotators.
  As a result of the rapid rotation, the cool giants in symbiotics should have
3-30 times larger mass loss rates. Our results suggest also that bipolar
ejections in symbiotics seem to happen in objects where the mass donors rotate
faster than the orbital period.
  All spectra used in our series of papers can be obtained upon request from
the authors.
