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Four families of generalizations of trigonometric functions were recentlyintroduced. In the paper the functions are transformed into four families oforthogonal polynomials depending on two variables. Recurrence relations forconstruction of the polynomials are presented. Orthogonality relations of thefour families of polynomials are found together with the appropriate weightfuctions. Tables of the lowest degree polynomials are shown. Numeroustrigonometric-like identities are found. Two of the four families of functionsare identified as the functions encountered in the Weyl character formula forthe finite dimensional irreducible representations of the compact Lie groupSp(4). The other two families of functions seem to play no role in Lie theoryso far in spite of their analogous `good' properties.

Four families of orthogonal polynomials of C2 and symmetric and antisymmetric generalizations of sine and cosine functions