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There are valid reasons to prefer radians, especially in calculus. The fact that it's related to arc length is something that never (directly) comes up.
by HWR_14 1mo ago
There are valid reasons to prefer radians, especially in calculus. The fact that it's related to arc length is something that never (directly) comes up.
- groundzeros2015 1mo agoEvery 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. For example when you do a Taylor series expansion the cos/sin are well approximated by x.
- HWR_14 1mo agoThat'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 . If 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.
- groundzeros2015 1mo agoYour awareness of a key relationship does not make it irrelevant. It happens all the time in math. the article acts like radians are arbitrary without discussing this key property.