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```					           RADIANS
Definition
An arc of length r subtends an
angle of one radian at the
centre of a circle of radius r

r           r
r
Proof
r        r   How do you calculate the length of an arc?
r
r = ø x 2πr
360º
r = 1 radian x 2πr
360 º
x 360 º       360r = 1 radian x 2πr
÷r            360 º = 1 radian x 2π
÷2            180 º = 1 radian x π    Or 180 º = π radians
π

π

180

So if ø is measured in radians
Then ø radians = ø x π
180
How many different angles can you write

2

r
r   Arc Length
r                               Angle in
Arc length = ø x 2πr
degrees
360º

Arc length = 2πrø
360º

Factorise r       Arc length = r 2πø
360º

Divide by 2       Arc length = r πø       Angle
180º      in
Arc length = rø
r       r
Area of Sector
r                                 Angle in
Sector area = ø x πr2
degrees
360º

Sector area = πr2ø
360º

Factorise r2      Sector area = r2 πø
360º

Factorise out ½   Sector area = ½r2 πø      Angle
180º    in
Sector area = ½r2ø
Examples
50° =    50° x π rad
180
Examples
2.7 rad =   2.7 x 180   degrees
π
Examples
40° = 40 x π
180
40° = 40π
180
9
10cm               Calculate the arc
length and sector area

Arc length = rө           Arc length = 10 x 1.2
Arc length = 12cm
Sector area = ½r2ө        Area = ½ x 100 x 1.2
Area = 60cm2

```
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