Taylor's 7th (I think XD) Review Blog

REVIEW TIME!!

The following information is a review 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 4cm and the central angle is .0098 radians. Find the area and the radius of the object.

Theta= .0098
S= 4 cm
K= ?
R= ?

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

4=Rx.0098

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

408.163 cm=R

Then divide .0098 from both sides to find out what R is. Make sure to put the length of measurements in the appropriate places and to round to the third place after the decimal.

K=1/2x408.163x4

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=816.326 cm^2

Finally, you just need 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 5x10^7 mi and the apparent size of the moon is 2000 radians. What is the diameter?

Theta=2000 radians
S= ?
R= 5x10^7 mi

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

S=5x10^7x2000

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

S= 100000000000 mi

Then you multiply 5x10^7 and 2000 and you get your answer.

That is what we learned in lesson 7.2.