This investigation extends a 25-point geometric system for defining a 25-point trigonometry whose properties are analogous to those of the trigonometry of the Euclidean plane. These properties include definitions of trigonometric functions arising from ratios of sides of right triangles, the relations of elements of a given triangle through the Law of Sines and the Law of Cosines, and the relations of trigonometric functions expressed through identities. The study also shows how the concepts of the 25-point trigonometry apply to a 49-point system and suggests the possibility of still other finite trigonometries. Finally, the study includes a description of a classroom presentation of finite trigonometry to college freshmen. (RP)