1 resource radian measure and arc length

RADIAN MEASUREARC LENGTH

AREA OF SECTORRADIAN MEASURE USE IN TRIGONOMETRY

Circular Measure

Properties of A Circle

What do we know about Circle? Minor

Sector

Arc

Area = πr2Circumference = 2πr/ πd

Finding Arc Length & Area of Sector

Radian Measure

The limitation of degree measurement requires another circular measure which is

radian.

The angle subtended at the centre of a circle by an arc are equal in length to the radius is 1 radian

Radian Measure

3 rad2 rad

r

3r

rO

P2r

r

r

AD

CP

AO

3 rad2 rad

r

3r

rO

P2r

r

r

AD

CP

AO

3.6 rad

E

r

s

rO

3.6r

rO

P

Length of arc APC = 2r

Length of arc APD = 3r

Length of arc APE = 3.6r

AOC = 2 radians AOD = 3 radians AOE = 3.6 radians

So, how do we determine the radian measure given the arc length and the radius of the circle?

Radian Measure

In general, if the length of arc, s units

and the radius is r units, then

For example:

If s = 3 cm and r = 2 cm, then

That is the size of the angle (θ) is given by the ratio of the arc length to the length of the radius.

Relation between Radian and Degree Measure

3.6 rad

E

r

s

rO

3.6r

rO

P

Consider the angle θ in a semicircle of radius r as shown below. Then,

We can conclude

Furthermore,

Convertion between Degree & Radian

DEGREE RADIAN

Relation between Radian and Degree Measure

Example 1:

Solution:

Relation between Radian and Degree Measure

Example 2:

Solution:

Classwork

References

Thong, Ho Soo, Msc, Dip Ed; Hiong, Khor Nyak, Bsc, Dip Ed; “New Additional Mathematics” pg. 280 - 292, SNP Panpac Pte Ltd, Singapore 2005.