Question 522806
If x is measured in radians, then the derivative of Sin[x] with respect to x is Cos[x].

Use the formula Sin [x degrees] = Sin [2π/360 x radians]
to calculate the derivative of Sin [x degrees] with respect to x.
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f(x) = sin(x), x in degrees
f(x) = sin(x*180/pi) radians
f'(x) = cos(x*180/pi)*(180/pi), x in degrees
f'(x) = (180/pi)*cos(x), x in radians
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Why does the resulting formula make calculus difficult if you insist on working with degrees instead of radians?
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It's more complicated because x is multiplied by a constant, (180/pi).
Degrees are "artificial" or arbitrary units, the same as gradients.
Radians are a function of the ratio of the arc length to the radius, so the units of the circle, cm, feet, miles, whatever, are canceled. Radians are "unitless" measure.
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