On the unit circle, if A is the area of the sector formed by a central angle of theta radians,
then A = theta
I don't understand this, can someone help?
Your formula is off by a factor of 2.
The angle $\displaystyle \theta$ is a section of the circle. So the area of the wedge is proportional to the angle $\displaystyle \theta$.
Thus
$\displaystyle \frac{\theta}{2 \pi} = \frac{A}{\pi (1)^2}$
(Remember this is the unit circle so r = 1.)
$\displaystyle A = \frac{\theta}{2}$
-Dan