How to calculate arc length in unit circle

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To calculate arc length in a unit circle, the formula s = rθ is used, where θ is in radians and r is the radius. In the case of a unit circle, r equals 1, simplifying the formula to s = θ. Knowledge of special angles in the unit circle is beneficial for quick calculations, but for arbitrary coordinates like x = 0.6 and y = 0.8, inverse sine may be necessary to determine the angle. The discussion emphasizes the importance of understanding both the formula and the relationships between coordinates on the unit circle. Mastery of these concepts allows for accurate arc length calculations without reliance on calculators or trigonometric tables.
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http://www.up98.org/upload/server1/01/z/cllb59cvnwaigmmar6b5.jpeg

What is the method of calculating arc length in In the image above .
x & y is known
Thanks .
 
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Feuilleton :
Obviously, the use of calculators and trigonometric tables is not allowed
 
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.
 
Ivan92 said:
There is a formula for it.

s = r θ, where θ is in radians.
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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