Area of Sector

In a circle with centre, \(O\) and radius \(r\) units, the formula for finding the

\(\text{Area of sector} = \frac{x^\circ}{360^\circ} \times \pi r^2 \text{ (part of the area of a circle)}\)

where \(x^\circ\) is the angle in degree, subtended by the arc at the centre of the circle of radius \(r\).

\(\text{Area of minor segment} = \text{Area of minor sector} - \text{Area of triangle}\)

\(= \frac{\theta}{360} \times \pi r^2 - \frac{1}{2} r^2 \sin(\theta^\circ)\)

Here \(\theta\) is the numerical measure in degrees of the smaller central angle, with \(0<\theta<180\). Evaluate \(\sin(\theta^\circ)\) in degree mode. For a diameter (\(\theta=180\)), the two segments have equal semicircular areas.

So how to find the area of the major segment?