There is a formula:
Area of segment of circle = r^2 (pi*theta/360) - (sin theta/2), where theta is a measure of corresponding arc in degrees.
Could you please explain how they introduce sine in this formula? why not cosine?
sin is introduced here because if you bisect the sector angle theta into two: theta/2,theta/2 then
sin(theta/2)=(width of half triangle)/radius
so we get side of triangle as 2*r*sin(theta/2)
now you have other two sides of triangle as r
apply heroes formula
then subtract this area from the sector area mentioned above
apply approximations and u will get ur result