Radians, arcs and sectors

The idea

$\pi$ radians $= 180^\circ$. In radians the formulae are short: arc length $s = r\theta$ and sector area $A = \frac{1}{2}r^2\theta$.

1. Convert degrees to radians by multiplying by $\frac{\pi}{180}$.
2. Use $s = r\theta$ and $A = \frac{1}{2}r^2\theta$ with $\theta$ in radians.
3. For a segment, subtract the triangle $\frac{1}{2}r^2\sin\theta$ from the sector.

Watch out $s = r\theta$ only works with $\theta$ in radians.