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?

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- May 22nd 2008, 10:54 AMgabrie30Quick Question
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? - May 22nd 2008, 11:00 AMMoo
- May 22nd 2008, 11:16 AMtopsquark
- May 22nd 2008, 11:19 AMtopsquark
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