To quote a really important comment posted by Eduardo Vasquez on the article:

> [...] all those formulas of derivatives and primitives of trig functions in standard calculus books assume that arguments are expressed in radians. Say, the derivative of sin(x) w.r.t. x is cos(x) --- that is only true if x is in radians. Otherwise, you would get an extra factor, due to the chain rule. [...]

(There are a few comments here that point this out, but they are nested pretty deep so I thought it was worth repeating.)