Sectors

-Formulas
K= 1/2 R^2 Theta

*Where K is the area of a sector, R is the radius, Theta is the central angle*

K=1/2 RS

*Where R is the radius and S is the arc length*



*KEY NOTES*


S =  R Theta or Theta = S/R
Theta = Apparent Size
R = distance between 2 objets 
S = Diameter


Example 1: A sector of a circle has an arc length of 6 cm and a area of 75 cm^2. Find its radius and the measure of its central angle.

S= 6cm
K= 75 cm^2
R= ?
Theta = ?

K=1/2 RS
S= R Theta

75= 1/2 R (6)
=75/3 = 3r/3
R=25 cm

S = R Theta
Theta = S/R
Theta = 6/25 rads

Step1) Write out what is given to you and what you are looking for
Step2) Write out the formulas you are going to need
Step3) Find the radius
Step4) Plug your givens into K=1/2 RS and solve for K
Step5) Find Theta
Step6) You are looking for Theta, so you have to isolate the Theta in the formula, by moving the R over to the other side by division
Step7) Plug into formula and solve


Example 2: Jupiter has an apparent size of .01 degrees when it is 8x10^8 Km from the Earth. Find the approximate diameter of Jupiter.

*Theta has to be in rads*

Theta= .01 degrees x pie/180 = .01/180 pie

R= 8x10^8
S=?

S=R Theta
S= (8x10^8)(.01/180 pie)
S= 139626.3402

Step1) Convert Theta to rads
Step2) Right out your givens and what you need
Step3) Find out what formula you are going to need to use
Step4) Plug into formula and solve