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.
Why does the resulting formula make calculus difficult if you insist on working with degrees instead of radians?
Thanks for any help you can offer!
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! 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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