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Norman Wildberger's rational trigonometry, introduces a new and simplified approach to trigonometry and a major restructuring of Euclidean geometry. It replaces cos, sin, tan and all those other transcendental trig functions with rational functions and elementary arithmetic.
Learn more about it from Norman's videos, which can be found on this page;
Norman Wildberger is an Associate Professor in mathematics at UNSW (University of New South Wales) in Sydney, Australia.
He is originally from Canada.
For more on all this see his website;