Length of an Arc and Area of a Sector (VCE SSCE General Mathematics): Flashcards

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Length of an Arc and Area of a Sector
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Definition of an arc

A curved section of a circle's circumference

Arc length formula (with radius rr, angle θ\theta)

s=πrθ180s = \frac{\pi r\theta}{180}

Definition of a sector

A wedge-shaped region of a circle with two radii and an arc

Sector area formula (with radius rr, angle θ\theta)

A=πr2θ360A = \frac{\pi r^2\theta}{360}

Definition of a minor sector

The smaller region when a circle is divided by two radii

Definition of a major sector

The larger region when a circle is divided by two radii

How to find major sector angle from minor angle θ\theta

360°θ360° - \theta

Denominator in arc length formula

180

Denominator in sector area formula

360

Units for arc length if radius is in cm

cm (linear units)

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