How would you find the area of the major sector and the major segment of a circle? Write the formulas.

(i) Area of the major sector: The major sector corresponds to the angle $(360^\circ - \theta)$, so its area can be found in two ways: $$\text{Area of major sector } OAQB = \pi r^2 - \text{Area of minor sector } OAPB$$ Alternatively: $$\text{Area of major sector} = \frac{360 - \theta}{360} \times \pi r^2$$ (ii) Area of the major segment: The major segment is the complement of the minor segment: $$\text{Area of major segment } AQB = \pi r^2 - \text{Area of minor segment } APB$$ Substituting the minor segment area formula: $$\text{Area of major segment} = \pi r^2 - \left(\frac{\theta}{360} \times \pi r^2 - \text{Area of } \triangle OAB\right) = \frac{360 - \theta}{360} \times \pi r^2 + \text{Area of } \triangle OAB$$ Note: The major segment area equals the major sector area plus the area of $\triangle OAB$, because the triangle is part of the major segment but not part of the major sector.