1 resource radian measure and arc length

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Transcript of 1 resource radian measure and arc length
 1. Radian measure
Arc length
Area of sector
Radian measure use in trigonometry
Circular Measure
2. Properties of A Circle
What do we know about Circle?
Minor Sector
Arc
Area = r2
Circumference = 2r/ d
3. Finding Arc Length & Area of Sector
4. 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
5. Radian Measure
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?
6. Radian Measure
In general, if the length of arc, s units and the radius is r
units, then
That is the size of the angle () is given by
the ratio of the arc length to the length of the radius.
For example:
If s = 3 cm and r = 2 cm, then
7. Relation between Radian and Degree Measure
Consider the angle in a semicircle of radius r as shown below.
Then,
We can conclude
Furthermore,
8. Convertion between Degree & Radian
DEGREE
RADIAN
9. Relation between Radian and Degree Measure
Example 1:
Solution:
10. Relation between Radian and Degree Measure
Example 2:
Solution:
11. Classwork
12. References
Thong, Ho Soo, Msc, Dip Ed; Hiong, Khor Nyak, Bsc, Dip Ed; New
Additional Mathematicspg. 280  292, SNP Panpac Pte Ltd, Singapore
2005.