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What is the length of the arc on the unit circle subtended by an angle of 120 degrees? Show all work.

  1. 2/3
  2. 1/3(pi)
  3. 2/3(pi)
  4. pi

I used an equation where the central angle equals the arc length divided by the radius. Since 120 degrees is 1/3 of the total circumference of 360 degrees (or 2pi), I chose the answer to be 2.

Is my answer correct? If not, please explain why.

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  • $\begingroup$ Are you saying that a third of $2\pi$ is $\frac13\pi$? $\endgroup$ – Arthur Apr 30 at 9:22
  • $\begingroup$ The answer is 3). The circumference of the unit circle is $2 \pi$ and you are taking it as $\pi$. $\endgroup$ – Kavi Rama Murthy Apr 30 at 9:22
  • $\begingroup$ @Arthur Now that you put it that way, I see where I made the mistake. $\endgroup$ – Bibliophile Apr 30 at 9:47
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Angle ,$ \theta$(in radians) = arc-length/ radius = $\frac{s}{r}$

We have $r=1$ and $\theta = 120^o = 2\pi/3$

So, $s=r\theta = 1.2\pi/3 = 2\pi/3$

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