It is well known that the four ancient Greek triangle centers and others have homogeneous barycentric coordinates that are polynomials in the sidelengths a; b; c of a triangle ABC. For example, the circumcenter is represented by the polynomial a(b2 + c2 - a2). It is not so well known that triangle centers having barycentric coordinates such as tanA : tanB : tanC are also representable by polynomials, in this case, by p(a; b; c) : p(b; c; a) : p(c; a; b), where p(a; b; c) = a(a2 + b2 - c2)(a2 + c2 - b2). This paper presents and discusses polynomial representations of triangle centers that have barycentric coordinates of the form f(a; b; c) : f(b; c; a) : f(c; a; b), where f depends on one or more of the functions in the set fcos; sin; tan; sec; csc; cotg. The topics discussed include innite trigonometric orthopoints, the n-Euler line, and symbolic substitution.