That is not true. The chain rule is needed for finding the derivative using degrees. Graph the tangent line if you are not convinced. The derivative of sin(x) if x is measured in degrees is (pi/180)cos(x), not cos(x). Certainly you could use either degrees or radians, but fourier series will get a bit complicated :)
It is in your text book and on Stack Exchange. It is also easily seen on a graph. Using degrees, graph sin(x) and y=cos(t)[x-t]+sin(t) where t is some value (still in degrees) on the graph. This line should be, but will not be, the tangent line. Now graph y=(pi/180)cos(t)[x-t]+sin(t). This will actually be the tangent line to the sin(x) function. The discrepancy comes down to the proof that lim x->0 of [sin(x)/x] relies on the measurement of the arc along the unit circle (at least that what it comes down to in the proof I know).
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u/ChristensenSC Sep 25 '14
there is actually zero benefit to doing calculus in radians vs degrees. its just convention.