In Figure 1.4.3, sector COB is part of a circle of radius $\cos \left(\mathrm{\θ}\right)$, the length of the segment OB. This sector is a fractional part of that circle, which has an area of $\mathrm{\π} {\cos }^2\left(\mathrm{\θ}\right)$. The fractional part of the area is the ratio of the angle $\mathrm{\θ}$ to $2 \mathrm{\π}$, the full circle. Hence, the area of sector COB is $\frac{\|\mathrm{\θ}\|}{2 \mathrm{\π}}\left(\mathrm{\π} {\cos }^2\left(\mathrm{\θ}\right)\right)\=\frac{\left|\mathrm{\θ}\right|}{2} {\cos }^2\left(\mathrm{\θ}\right)$.