The only definition of the trigonometric function required is that sin (x) = opp/adj. It's just a ratio, nothing else. The students could have called this ratio

The only definition of the trigonometric function required is that sin (x) = opp/adj. It's just a ratio, nothing else. The students could have called this ratio "snoo" and the proof would have still worked. The proof is rigorous. The original article explains this, and why it's not circular.