How to calculate arc length in unit circle

[subuntu]

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 .

 

[subuntu]

Feuilleton :
Obviously, the use of calculators and trigonometric tables is not allowed

 

[Ivan92]

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.

 

[eumyang]

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?

 

[CellCoree]

To calculate the arc length in a unit circle, we can use the formula: arc length = radius * central angle. In the image provided, the radius is 1 unit (since it is a unit circle) and the central angle is given by the ratio of x to y. Therefore, the arc length can be calculated by multiplying 1 unit by the ratio of x to y. For example, if x = 0.5 and y = 1, the central angle would be 0.5 radians and the arc length would be 0.5 units. This formula can be applied to any unit circle, as long as the radius and central angle are known.