See also:
WildTrig85: Understanding uniform motion: are radians really necessary? (beginning, first part)
In this video we inquire into the meaning, use and logical structure of so-called "radian measure". The history of this idea is not so old, and as opposed to what high school students are taught, the theory relies heavily on the calculus. In fact the underlying theory of arc lengths of curves, as a pure mathematical theory, is a notorious sleight of hand.https://www.youtube.com/watch?v=CnQXRdgN_7I
The distinction between useful and powerful applied mathematics
that we use in our technological world and the ideal fantasies of modern pure mathematics is very relevant for this discussion, and we will spend some time trying to clarify the important distinctions here.
And we look at the circular functions from the radian point of view, which are stalwart objects for modern analysis.
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