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Arc Length Flashcards
GCSE Mathematics (Edexcel) 1MA1
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Arc length
The distance along the curved part of a circle between two points.
Formula for arc length
Arc length = (θ / 360) × 2πr, where θ is the angle in degrees and r is the radius.
What does θ represent in the arc length formula?
θ represents the angle subtended by the arc at the centre of the circle, measured in degrees.
What does r represent in the arc length formula?
r represents the radius of the circle.
Unit of arc length
The unit of arc length is the same as the unit of the radius (e.g., cm, m).
Relationship between arc length and circumference
Arc length is a fraction of the circle's circumference, determined by the angle θ.
Circumference of a circle
Circumference = 2πr, where r is the radius.
How to find the angle θ if arc length and radius are known?
Rearrange the formula: θ = (Arc length / (2πr)) × 360.
Sector of a circle
A sector is the region of a circle enclosed by two radii and the arc between them.
Key step in solving arc length problems
Ensure the angle θ is in degrees and the radius is in the same unit as the required arc length.
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