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This guy claims to have revolutionized trig. Has anyone heard about it? Incredible, if it's for real.
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I just looked through the first chapter.
There are some nice points that many calculations can be simplified if you are computing different quantities, such as the squares of lengths and sin^2(angle) instead of the angle. However, there is a lot of hype, and there are numerous misstatements about the point of trigonometry and how it fits into the history of mathematics and curriculum. We would still need classical coordinate systems and classical trigonometry for calculus, analytic geometry, differential geometry, and Fourier analysis, among other things. Using the squares of lengths and sin^2(angle) also makes many simple calculations and relationships become complicated, such as adding two lengths or angles.
It's amusing, but it should not replace trigonometry.