Out with the old trigonometry

Mathematics students have cause to celebrate. A University of New South Wales academic, Dr Norman Wildberger, has rewritten the arcane rules of trigonometry and eliminated sines, cosines and tangents from the trigonometric toolkit.

I have not read the book, "Divine Proportions," and cannot judge its value. However, I do have a comment on the notion that we could somehow dispense with teaching the trig functions in high school or college. Trig functions are not just about figuring triangles. There are many mathematical concepts that make use of trigonometry and have no obvious connection to triangles. Engineers and many other practical users of mathematics rely on these functions for many basic calculations. Is it possible to supplant the trig functions with something else, in such a way that it would generalize to all the other current uses of trigonometry in higher math? If so, how do we make the transition? Can we really have one generation of engineers who understand and write things in terms of sine and cosine, and another generation immediately following who have no knowledge of these things? Or one branch of the field that uses one set of definitions and another branch that can't communicate with the first because it uses another set of definitions? I won't say it's impossible to establish a new paradigm, nor that it should not be done. Just that it seems extremely difficult. Proceed with caution before eliminating something so basic from the mathematics curriculum. If it really is a good idea, work it from the top down--get the graduate schools on board first, then the undergraduate schools, etc. so the reliance on the old system can be weaned in an orderly manner.

If anyone is familiar with Wildberger's ideas, please add some comments.