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?
sector area=(pi*(r^2))(theta)/360
sin is introduced here because if you bisect the sector angle theta into two: theta/2,theta/2 then
therefore
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