1 resource radian measure and arc length

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RADIAN MEASURE ARC LENGTH AREA OF SECTOR RADIAN MEASURE USE IN TRIGONOMETRY Circular Measure

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This presentation explains the connection the radian and degree measure in circular measure.

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.