Sectors of Circles:

There are three formulas you can use to find your variables/missing pieces.

One you can use is:

K=1/2 (r^2) Θ

Another formula you can use is:

K=1/2 r (s)

These two formulas give you your answers in radians.

Another formula you can use is:

S=r Θ

When looking for apparent size, you mainly use this formula.

In all of these:

R= Radius (distance between two objects)

Θ= Central Angle (apparent size)

S= Diameter of object (arc length)

K=Area

Number 4 from homework assignment (2 September 2011): A sector of a circle has arc length 2 cm and central angle 0.4 radians. Find its radius and area.

Write down what is given:

S=2

Θ=0.4

Now we’re looking for the radius and the area (K).

Since we know S and Θ, we use the formula: s=r Θ to find r.

When using this formula, you need to solve for the variable first, so it’ll look like this: s/ Θ=r, plugging in the numbers: 2/0.4=5 so r=5.

The next variable we need to solve for is K, to find the area. To find the area, use the formula: K=1/2 r(s).

So, K=1/2(5)(2) ; K=5

Answer:

R=5

K=5

S=2

Θ=0.4

Kbye ;)