  We consider a class of trigonometric solutions of WDVV equations determined
by collections of vectors with multiplicities. We show that such solutions can
be restricted to special subspaces to produce new solutions of the same type.
We find new solutions given by restrictions of root systems, as well as
examples which are not of this form. Further, we consider a closely related
notion of a trigonometric $\vee$-system and we show that their subsystems are
also trigonometric $\vee$-systems. Finally, while reviewing the root system
case we determine a version of (generalised) Coxeter number for the exterior
square of the reflection representation of a Weyl group.
