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How to calculate arc length in unit circle

  1. Dec 7, 2011 #1
    http://www.up98.org/upload/server1/01/z/cllb59cvnwaigmmar6b5.jpeg [Broken]

    What is the method of calculating arc length in In the image above .
    x & y is known
    Thanks .
     
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Dec 7, 2011 #2
    Feuilleton :
    Obviously, the use of calculators and trigonometric tables is not allowed
     
  4. Dec 7, 2011 #3
    There is a formula for it.

    s = r θ, where θ is in radians.

    You shouldn't need a Trig table, you should know the table. The angles in the unit circle are special angles which you should know by heart.
     
  5. Dec 7, 2011 #4

    eumyang

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    Homework Helper

    It looks like the OP already knows this, because outside of the circle he/she writes: "arc length = θ = ?" (since r = 1).

    As for knowing the table, that is helpful ONLY if x, y, and r form one of the two special triangles. If x = √3/2 and y = 1/2, then sure, we can find the arc length no trouble. But what if x = 0.6 and y = 0.8? We would need to make use of the inverse sine, wouldn't we?
     
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