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I forgot my secondary school maths, so I need to ask to confirm.

Arc Length = Radius*(Angle In Radian)

Is it correct?

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Yes. That is correct. –  Daryl Sep 26 '12 at 8:01
    
This might be enlightening: mathwarehouse.com/trigonometry/radians/… –  brendansullivan07 Sep 26 '12 at 8:02

2 Answers 2

up vote 3 down vote accepted

Yes. This works because $C = 2\pi R$ and, coincidentally, there are $2\pi$ radians in one full rotation. Clearly, a fraction of a full rotation produces a fraction of circumference.

To be fair, your equation is in fact the definition of radian.

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It's approximately correct only because you assume that the arc is the base of a triangle... It only works where you can say that sin(θ) is approximately θ. For small angles only. General solution using $sin^{-1}$ is also an approximation tho because of the curvature. If it was me, I would calculate the perimeter with the given Radius and calculate the ratio corresponding to the ratio $\frac{360}{\theta}$.

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1 radian is the arclength equivalent to the radius of the circle, by definition. –  Daryl Sep 26 '12 at 8:00
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Oh... My bad... –  mak Sep 26 '12 at 8:03

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