No one is obligated to be interested in everything, but I don't understand why you are bragging about your lack of intellectual curiosity about precise mathematical thinking. The difference between triangle trigonometry and unit circle trigonometry is well known to mathematics and important for constructing correct proofs (see the OP's cited Zimba's paper for a recent explanation), and deserves a name for clarity in exposition.
If anything, "trigonometric" is the word they should have avoided, since, even though the word is etymologocally closely associated with triangles as they said, it is also commonly used to refer to exactly the thing they are trying to avoid -- dependency on the Pythagorian theorem, which was the spource of all the confusion and fuss and terrible media reporting when they first published their proof and referred to an ill-defined statement in a 100 year old textbook.
There are hundreds of old proofs of Pythagorean Theorem. I'm sure you can find one that satisfies you. For those of us who enjoy new ideas that push back the intellectual frontier, this paper is very nice.
If anything, "trigonometric" is the word they should have avoided, since, even though the word is etymologocally closely associated with triangles as they said, it is also commonly used to refer to exactly the thing they are trying to avoid -- dependency on the Pythagorian theorem, which was the spource of all the confusion and fuss and terrible media reporting when they first published their proof and referred to an ill-defined statement in a 100 year old textbook.
There are hundreds of old proofs of Pythagorean Theorem. I'm sure you can find one that satisfies you. For those of us who enjoy new ideas that push back the intellectual frontier, this paper is very nice.