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I'm aware that the angle in radians is 1 when the arc length is equal to the radius. However, I wonder if this is exactly where radians come from. Have we set radians like this (like we set $i^2$ to $-1$) or is there something more to it?

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    $\begingroup$ Amongst other things, the derivatives of the $\sin$ and $\cos$ functions become much easier when the arguments are radians rather than degrees or other unit. $\endgroup$ May 4 at 22:26
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According to Earliest Known Uses of Some of the Words of Mathematics, the term "radian" was coined independently by James Moore and William Thompson (Lord Kelvin) in the 19th century.

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