Major and Minor Regions

What is Major and Minor Regions?

The pair of regions a chord or a pair of radii divides a circle into, the smaller being called minor and the larger major. A minor sector has central angle theta with theta less than pi, while the corresponding major sector has the reflex angle 2 pi minus theta, and the two areas add to the whole disc. The safest route to a major region is to subtract the minor one from the whole circle; substituting the reflex angle directly into the sector or segment formula also works, and for a segment it works because the sine of a reflex angle is negative.

This definition is part of the Circular Measure chapter in Cambridge O Level Additional Mathematics.

Concepts related to Major and Minor Regions

• reflex angle \(2\pi-\theta\)
• whole disc minus minor
• \(\sin(2\pi-\theta)=-\sin\theta\)