Chain rule trig functions proof
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Chain rule trig functions proof

[From: ] [author: ] [Date: 11-09-26] [Hit: ]
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)),......
"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

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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.

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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
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