Sectors (Leaving Cert Mathematics): Flashcards

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Sectors
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Arc length formula (radians)

s=rθs = r\theta

What does θ\theta represent in s=rθs = r\theta?

Angle in radians

Sector area formula (radians)

A=12r2θA = \frac{1}{2}r^2\theta

Arc length formula (degrees)

l=2πr×Θ360l = 2\pi r \times \frac{\Theta}{360}

Sector area formula (degrees)

A=πr2×Θ360A = \pi r^2 \times \frac{\Theta}{360}

Calculate arc length: r=10r=10 cm, θ=π4\theta=\frac{\pi}{4}

5π2\frac{5\pi}{2} cm

Calculate sector area: r=6r=6 cm, θ=π3\theta=\frac{\pi}{3}

6π6\pi cm²

When are sector formulas simpler?

When angle is in radians

Convert 46° to radians (3 s.f.)

0.803 radians

What is rr in s=rθs = r\theta?

Radius of the circle

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