Block 3

Radian Measure

What is to be learned?

• What a radian is• How to convert between radians and

degrees

Units

Lengthm , cm , km , miles , inches , feet etc.

Weightg , kg , stones , pounds, ounces etc

AnglesDegrees

Introducing Radian Measure

Want arc = radius The Same Length

Introducing Radian Measure

Want arc = radius

Introducing Radian Measure

Want arc = radius

1 radian

Radians and Degrees

Some Sums (or sum somes?)

1 radian 3600

Cross multiplying

r

2πr=

2π radians = 3600

π radians = 1800

1 radian ~ 570

Radians and Degrees

Some Sums (or sum somes?)

1 radian 3600

Cross multiplying

r

2πr=

2π radians = 3600

π radians = 1800

1 radian ~ 570

Radians to Degrees

π radians = 1800

radians degrees

π = 180

1 =

radians Degrees

180π

X 180π

Radians Degrees

= 450

X 180π

π 4 radians

π 4

X 180π

= 180 π4π

Radians Degrees

= 1500

X 180π

5π 6 radians

5π 6

X 180π

= 900 π6π

Degrees Radians

radians

X π

180

1000

100 1

= 100 π180

X π

180

10

18

= 5 π 9

cOther Way Round!

X ?

Degrees Radians

radians

X π

180

2400

240 1

= 240 π180

X π

180

24

18

= 4 π3

12

9

Radian Measure

Another unit for measuring angles π radians = 1800

1 radian ~ 570

Radians Degrees

= 1350

X 180π

3π 4 radians

3π 4

X 180π

= 540 π4π

Degrees Radians

radians

X π

180

2000

200 1

= 200 π180

X π

180

20

18

= 10 π 9

x

4 cm8cmO

A = 4/8

= 0.5so x = 300

HSin x = 0/H

Find size of angle x in radians

radians= π 6

Key Question