How to calculate arc length in unit circle

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SUMMARY

The arc length in a unit circle can be calculated using the formula s = r θ, where θ is in radians and r is the radius. In the case of a unit circle, the radius r equals 1, simplifying the formula to s = θ. Knowledge of special angles and their corresponding sine and cosine values is crucial for determining θ when given coordinates (x, y). For non-special angles, the inverse sine function may be necessary to find θ.

PREREQUISITES
  • Understanding of the unit circle and its properties
  • Familiarity with radians and their conversion from degrees
  • Knowledge of trigonometric functions, particularly sine and cosine
  • Ability to use inverse trigonometric functions for angle calculation
NEXT STEPS
  • Study the derivation and applications of the arc length formula s = r θ
  • Learn how to convert between degrees and radians effectively
  • Explore the properties of special triangles in relation to the unit circle
  • Practice using inverse sine and cosine functions to find angles from coordinates
USEFUL FOR

Students in mathematics, educators teaching trigonometry, and anyone interested in understanding the geometric properties of circles and trigonometric functions.

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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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