“It’s a ‘natural’ derived measurement, with no need for a physical or literal standard to represent it.”
Yes, but it’s still arbitrary. A standard being arbitrary or not doesn’t depend on whether it’s related to a physical object. We can choose to use radians or degrees (or some other standard) to measure angles, and all of them accomplish exactly the same thing. Therefore, our use of one or the other as a standard is by definition arbitrary.
“A ‘degree’ can be anything, of any size value...”
No, by definition it can’t. If you decide to make a “degree” that is 1/100 of the angular total of a circle, then it’s not a “degree” anymore, it’s something else. Either way, no matter what we would decide to subdivide the circle into in order to get a “degree”, it would also give us something that had “no need for a physical or literal standard to represent it”. You don’t need a physical circle or any material object to derive a degree, it’s a purely mathematical concept, just like a radian.
“The trigonometry would be the same, jut with a different set of standards.”
Yes, exactly correct. So to get back to the point, since the math is exactly the same no matter what standard of measurement you use, what exactly is the relevance of you suggesting that I use radians? The problem remains exactly the same.
Radians are now the ‘SI’ unit of angular measurement.
In the future, we will all be using Radians along with the Metric System of measurements.
The term ‘degree’ will be relegated to temperature measurements only............