This review of Wildberger's book at https://philarchive.org/archive/FRADPR says the point isn't that the PhD mathematician finds trig hard, but rather to beginners:
> ... very becoming-numerate generation invests enormous effort in the painful calculation of the lengths and angles of complicated figures. Surveying, navigation and computer graphics are intensive users of the results. Much of that effort is wasted, Wildberger argues. The concentration on angles, especially, is a result of the historical accident that serious study of the subject began with spherical trigonometry for astronomy and long-range navigation, which meant there was altogether too much attention given to circles. ...
> Having things done better is one major payoff, but equally important would be a removal of a substantial blockage to the education of young mathematicians, the waterless badlands of traditional trigonometry that youth eager to reach the delights of higher mathematics must spend painful years crossing
Cook isn't proving results about trig functions/identities; they're proving results about software. Software can never correctly implement trig functions; it must always approximate, and that is the reason it's hard to verify.
In contrast, arithmetic on rational numbers can be implemented exactly; at least, up to the memory limits of the machine (e.g. using pair of bignums for numerator/denominator)
bigbillheck|3 years ago
eesmith|3 years ago
> ... very becoming-numerate generation invests enormous effort in the painful calculation of the lengths and angles of complicated figures. Surveying, navigation and computer graphics are intensive users of the results. Much of that effort is wasted, Wildberger argues. The concentration on angles, especially, is a result of the historical accident that serious study of the subject began with spherical trigonometry for astronomy and long-range navigation, which meant there was altogether too much attention given to circles. ...
> Having things done better is one major payoff, but equally important would be a removal of a substantial blockage to the education of young mathematicians, the waterless badlands of traditional trigonometry that youth eager to reach the delights of higher mathematics must spend painful years crossing
Whether that's correct is different. https://handwiki.org/wiki/Rational_trigonometry seems to give a good description of opposing views.
chriswarbo|3 years ago
In contrast, arithmetic on rational numbers can be implemented exactly; at least, up to the memory limits of the machine (e.g. using pair of bignums for numerator/denominator)