How to find the sector of the circle

How to find the sector of the circle

Formulas:
1. s=(r)(theta)
(s= arch length) (r= radius) (theta= central angle)

2. k= (1/2)(r^2)(s)
(k= area of the sector)

3. k= (1/2)(r)(s)

Next here are your steps:
1. find out what is given.. for example s=? r=? k=? and theta=?
You must find at least two of these in order to figure out this problem.

2. you are going to want to make sure that theta is in radians.
if theta is in degrees then you need to multiply that by (pie/180) to convert degrees into radians.

3. next, you are going to need to choose one of the formulas to plug into.
you want to choose the formula that works best with the problem.
for example if you have s= 4 cm and k= 36 cm you are not going to want to choose formula #1.
you would want to choose formula #3.

4. then, after you find one of the missing variables you will have one more variable still to find.
so, you are going to plug into another equation that fits the found variables and plug into the appropriate equation.

Here is an EXAMPLE:
A sector of a circle has an arc length of 4 cm and an area of 52 cm^2. Find its radius and the measure of its central angle.

So now follow the steps..
What are the given variables?
s= 4cm k=52cm^2 r=? theta=?

Now you must use the appropriate formula
formula #3 will work the best. [k=(1/2)(r)(s)]
52cm^2=(1/2)(r)(4)
52cm^2=2r
r= 26cm

Now that you found the answer for the variable r you can plug into another formula to find theta.
the best fit formula to find theta is formula #1 [s=(r)(theta)]
4cm= (26cm)(theta)
theta=(1/6 radians)

This is how you find the sector of the circle.