Radians, Arc Length, and Sector Area

$\pi$ rad = 180°. Degrees → radians: × $\frac{\pi}{180}$. Radians → degrees: × $\frac{180}{\pi}$.

• Arc length: $s = r\theta$
• Sector area: $A = \frac{1}{2}r^2\theta$
• Segment area: $A = \frac{1}{2}r^2(\theta - \sin\theta)$

($\theta$ in radians)

$r = 10$ cm, $\theta = \frac{\pi}{3}$.

Arc: $s = 10 \times \frac{\pi}{3} = \frac{10\pi}{3} \approx 10.5$ cm.

Sector: $A = \frac{1}{2}(100)(\frac{\pi}{3}) = \frac{50\pi}{3} \approx 52.4$ cm².

Segment: $A = \frac{1}{2}(100)(\frac{\pi}{3} - \sin\frac{\pi}{3}) = 50(1.047 - 0.866) = 9.06$ cm².