# Quick Question

• May 22nd 2008, 10:54 AM
gabrie30
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?
• May 22nd 2008, 11:00 AM
Moo
Hello,

Quote:

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
• May 22nd 2008, 11:16 AM
topsquark
Quote:

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
• May 22nd 2008, 11:19 AM
topsquark
Quote:

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