A circle, centre O, has two radii OA and OB. The line AB divides the circle into two regions whose areas are in the ratio 3:1. If the angle AOB is theta (radians), show that:
theta - sintheta = pi/2
Well, the area is evidently 1/4 (pi*r^2).
In class we were told area = r^2(theta-sintheta).
Using this we get 1/4(pi*r^2) = r^2(theta-sintheta) so 1/4pi = (theta-sintheta), i.e. theta-sintheta = pi/4 not pi/2.... what have I done wrong?
