1
$\begingroup$

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

Arc Length = Radius*(Angle In Radian)

Is it correct?

  • 3
    Yes. That is correct.2012-09-26
  • 1
    This might be enlightening: http://www.mathwarehouse.com/trigonometry/radians/s=r-theta-formula-equation.php2012-09-26

2 Answers 2

3

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.

-1

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 $\frac{360}{\theta}$.

  • 1
    1 radian is the arclength equivalent to the radius of the circle, by definition.2012-09-26
  • 1
    http://en.wikipedia.org/wiki/Radian2012-09-26
  • 0
    Oh... My bad...2012-09-26