  Four families of generalizations of trigonometric functions were recently
introduced. In the paper the functions are transformed into four families of
orthogonal polynomials depending on two variables. Recurrence relations for
construction of the polynomials are presented. Orthogonality relations of the
four families of polynomials are found together with the appropriate weight
fuctions. Tables of the lowest degree polynomials are shown. Numerous
trigonometric-like identities are found. Two of the four families of functions
are identified as the functions encountered in the Weyl character formula for
the finite dimensional irreducible representations of the compact Lie group
Sp(4). The other two families of functions seem to play no role in Lie theory
so far in spite of their analogous `good' properties.
