Page 56 - Focus SPM 2022 - Additional Mathematics

Additional Mathematics SPM Chapter 1 Circular Measure

1.1 Radian SPM Tips
× π
180°
A Relating angle measurement in
radian and degree
degree radian
1. Assume a circular wire is cut along the radius of
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circle. Each piece of the wire obtained will have 180°
an arc of the same length as the radius of the × π
circle.
3 2 1
4 1 Convert the angle 40° to the angle in radians expressed
Piece of wire (a) in terms of π,
5 6 (b) without involving π.

2. Observe that the angle subtended by each piece Solution
of wire at the centre of the circle is always 57.3° (a) 40° = 40° × π 2 rad
1
or one radian. 180°
s = 2 π rad
9

r θ radian Alternative Method
1 radian r
= 57.3º 180° = π rad
r
40° = q
3. One radian is defined as the measure of the angle 40° × π
subtended at the centre of a circle if the arc length q = 1 180° 2 rad
s is equal to the radius r, that is s = r. 2 2
= π rad = π c
4. The angle in radian is equal to the ratio of the 9 9
arc length to the radius of a circle which is SPM Tips
s
q = .
r Angles in radians is marked with abbreviation “rad”,
or superscript letter c or r.
5. The angle of one complete revolution in degrees
and radians are 360° and 2π radian respectively. 3.142
1
Therefore, the relationship between the angle (b) 40° = 40° × 180° 2 rad
measurements in degrees and radians can be = 0.6982 rad = 0.6982 r
expressed as 180° = π radian.
SPM Tips Form 5
360º = 2π radian
Generally, the value of π used is 3.142.

C
C C A L C U L A T O R Corner
6. Using the relationship of 180° = π radian, the
following method can be used to convert angles The following type of calculator can be used to convert the
in degrees to radians and vice versa. angle 40° to an angle in radian:
(a) Angles in degrees are converted to the angles Casio FX-570MS: Press MODE 4 times, choose 2 ,
in radians by multiplying π . press 4 0 , SHIFT , Ans , choose 1 , press = .
180° Casio FX-570ES: Press SHIFT , SETUP , choose 4 ,
(b) Angles in radians are converted to the angles press 4 0 , SHIFT , Ans , choose 1 , press = .
in degrees by multiplying 180° .
π Try Questions 1 – 2 in ‘Try This! 1.1’

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