"Use the Chain Rule to show that if x is measured in degrees, then d/dx (sinx) = pi/180*cosx."
How would I do this? :P
How would I do this? :P
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If x were in radians, it is correct to say that d/dx (sinx)= cosx.
Assuming that x is actually in degrees, to get an equivalent radian value you would write pi/180 * x radians = x degrees.
But in terms of calculus, it matters that x is a different number than pi/180 * x because in calculus, differentiation of trigonometric functions assumes that you are using radians.
So d/dx (sinx) has to be rewritten as d/dx (sin(pi/180 * x)), which by the chain rule equals cos(pi/180 * x) times pi/180, and this can be rewritten as pi/180*cosx.
Assuming that x is actually in degrees, to get an equivalent radian value you would write pi/180 * x radians = x degrees.
But in terms of calculus, it matters that x is a different number than pi/180 * x because in calculus, differentiation of trigonometric functions assumes that you are using radians.
So d/dx (sinx) has to be rewritten as d/dx (sin(pi/180 * x)), which by the chain rule equals cos(pi/180 * x) times pi/180, and this can be rewritten as pi/180*cosx.
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x in degrees ---> sin x = sin[(pi/180)x] in radian ----> d/dx (sin[(pi/180)x]) = (pi/180)cos[(pi/180)x] in radian or (pi/180)cosx in degrees