Every part of calculus with trig functions relies on this fact! The rate of motion along a circle is approximately linear at the same speed when described in radians.
replyFor example when you do a Taylor series expansion the cos/sin are well approximated by x.
That's why I put "directly" in my original post. All the nice functions in calculus rely on that fact, but that fact itself is almost never used or useful by itself .
replyIf I were writing the article I would focus on the benefits for derivatives and integration and other things that are slipping my mind at the moment. I wouldn't waste time going down the rabbit hole of why.
At least not for an article aimed at this type of audience.
Your awareness of a key relationship does not make it irrelevant. It happens all the time in math.
replythe article acts like radians are arbitrary without discussing this key property.