Taylor's Blog 2

The following information is based on section 7.2 of my Advanced Math notes.

These are the formulas that you will need to work the following problems and equations.

S=RTheta(This is a circle with a line going horizontally through it)

k= 1/2r^2theta

k= 1/2rs

S stands for the arc length of the equation/formula.
R stands for the radius of the equation/formula.
Theta stands for the central angle of a problem.
K stands for the area of a sector.

Yet, sometimes you will not just be ask to find the arc length . They will sometimes call s, r, and
Theta other things in some word problems.

Theta is sometimes called the apparent size.

S is sometimes called the diameter of the object.

R is some times called the distance between the objects.

IMPORTANT NOTE THETA MUST BE IN RADIA NOT DEGREES!!

Now lets apply what we just learned into the following problems.

The arc length of an object is 6cm and the central angle is .0045 radians. Find the area and the radius of the object.

Theta= .0045
S= 6 cm
K= ?
R= ?

First identify what you know from the problem and what you need to find out.

6=Rx.0045

Next, chose one of the formulas and fill in what you can. Lets find R first since it iis easier to find. Then fill in the appropriate places with the right numbers.

5.9955 cm=R

Then subtract .0045 from both sides to find out what R is. Make sure to put the length of measurements in the appropriate places.

K=1/2x5.9955x6

Now lets use one of the K equations to find the area of the object. So once more fill in the appropriate areas with the right numbers.

K=17.9865 cm^2

Finally, you just need to to multiply the appropriate numbers and this is what you should get as your answer.

Ok lets try this problem next.

The distance between the moon and Earth is 4x10^3 mi and the apparent size of the moon is 5000 radians. What is the diameter?

Theta=5000 radians
S= ?
R= 4x10^3 mi

First, write down what you do know from the problem and what you need to find.

S=4x10^3x5000

Then place the information into a problem so that you can work it out.

S= 20000000 mi

Then you multiply 4x10^3 and 5000 and you get your answer.

That is what we learned in lesson 7.2.