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Define functions similar to those trigonometric. The sweeping vector out from the origin now varies in both its arc around from zero radians as well as its corresponding distance to the side of the polygon.

I believe these "polygonometric" functions are continuous. As s-->oo, the polygonometric functions approach the trigonometric. The relation of polygonometric functions with finite s to trigonometric functions may demonstrate great utility.

Has this idea been introduced before? What might be some of the applications for polygonometric functions?