His claim is that sin and cos in calculus are often introduced independently of geometry, as math for engineers is non rigorous, and the connection to triangles is a magical coincidence.
See also "Early vs Late Transcendentals" in calculus pedagogy.
Re:Stacking Triangles for Fun and Profit
by munchler on Thursday April 11, 2024 @02:06PM
(#40005036)
I agree, and the linked Wikipedia page starts out with the obvious definitions as well:
In mathematics, sine and cosine are trigonometric functions of an angle. The sine and cosine of an acute angle are defined in the context of a right triangle: for the specified angle, its sine is the ratio of the length of the side that is opposite that angle to the length of the longest side of the triangle (the hypotenuse), and the cosine is the ratio of the length of the adjacent leg to that of the hypotenuse.
Am I just misunderstanding something about this articles motivation? I’m pretty sure I learned the unit circle in high school trig, possibly even 7th grade geometry although my memory that far back is fuzzier; but we did lots of geometric constructions with straightedge and compass, and did basic geometric proofs using complementary angles etc, and my teacher was obsessed with triangles. I didn’t learn about series until Calc 2 in early undergrad.
I still use the unit circle to reconstruct various trig properties from memory.