1. Quick 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?

2. Hello,

Originally Posted by gabrie30
For a circle of radius 2, a central angle of 45 subtends an arc whose length s is 90.

Is this true or false? Why?

My guess is that its false and that the arc is (2X(PI/3))
This is indeed false, but I would say the answer is pi/2.

45/360=1/8

The perimeter is 2*pi*2=4*pi

--> length of the arc is (4*pi)/8

3. Originally Posted by gabrie30
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?
If you want to ask a new question, post it in a new thread. Do not simply edit over the old one.

-Dan

4. Originally Posted by gabrie30
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