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.
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