What is the formula of sector area?

What is the formula of sector area?

① The original formula: s sector = θ / 360 °× s circle = θ / 360 °× 2 π R & # 178;, where R is the radius of the circle and θ is the angle of the center of the circle. This is easy to understand, that is to calculate the area of the circle, then calculate the sector, and multiply it by the proportion of the sector to the total area. However, this method is not widely used
② The formula of curved triangle: s sector = 1 / 2 × LR, where l is the arc length of the sector and R is the radius of the circle. The good point of this formula is that it is very similar to the formula of triangle area, that is, the sector is regarded as a triangle whose bottom edge is bent into an arc, and the area is still 1 / 2 of the bottom multiplied by the height
③ The expression of radius and radian under radian system: s sector = 1 / 2 α R & # 178;, where α is the radian of the center angle of the circle. It can be directly derived from the definition of radian, α r = l (arc length)