Page 30 - Spotlight A+ SPM Additional Mathematics Form 4 & 5

Form
5
Chapter 1 Circular Measure Additional Mathematics
1.1 Radian Example 1 CHAP.

Relating angle measurement in radian and Convert the angle in the unit of radian to the 1
degree degree. [Use π = 3.142]
(a) 1.15 radian (b) 5π radian
6
1. In circular measures, the angle can be measured Solution:
in 2 units, which are (a) π rad = 180°
(a) degree (°) and minute (ʹ). 180°
(b) unit of radian (in or not in the terms of π). 1.15 rad = 1.15 × π
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180°
2. Radian involves the angle that related with the = 1.15 × 3.142
radius and circumference of a circle. = 65.89°
3. The diagram below shows the angle in degree (b) π rad = 180°
and minutes and radian while the radius have 5π rad = 5π × 180°
the same length. 6 6 π
5
= × 180°
6
= 150°
57° 17' 1 rad
O O Alternative Method
Substitute π =180° into the expression,
5π 5(180°)
6 = 6 = 150°
In degree and minute In radian
57° 17ʹ = 1 rad Try question 1 in Formative Zone 1.1

4. 1 radian is a measurement of an angle subtended Example 2
about the centre of a cirlce such as the arc length
is the same as the length of radius of circle. Convert
(a) 30° into radian unit, in term of π.
A (b) 200° into radian unit.
r r [Use π = 3.142]
Solution:
1 radian B
O r (a) 180° = π rad
30° = 30° × π
180°
= π rad
5. Hence, angle subtended about the centre of a 6
circle, ˙AOB is 1 radian if the arc length of AB is Alternative Method
equal to the radius of the circle. Substitute 180° = π into the expression,
180° π
AB = OA = OB = r 30° = = rad
6 6
6. The relationship between the measurement of (b) 180° = π rad
angle in radian with degree is 200° = 200° × π
180°
2π rad = 360° 200° = 200° × 3.142
π rad = 180° 180°
= 3.49 rad
7. The conversion of angle measurement in the degree Try question 2 and 3 in Formative Zone 1.1
to the radian and vice versa are as follow:
180°
× Calculator
π
Recheck the answer in Example 2(b) by using
Radian Degree calculator,
× π 1. Press 2 0 0 × SHIFT EXP ÷ 1 8 0 =
180° 2. The screen will display 3.490658504

1.1.1 217

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