What is there in the derivation of the Taylor/Maclaurin series for #sin(x)# that determines if the series assumes #x# is radians or degrees?
If the angle is not measured in radians, then the differentiation rule
In establishing (proving) that rule we use
That is also not true if
And that's because proving
If the central angle
You could also just say that the idea of the MacLaurin series for
When you do
But this is just a quick check. The actual proof might not be like this; I don't remember how it actually went.