Page 58 - Focus SPM 2022 - Additional Mathematics

Additional Mathematics SPM Chapter 1 Circular Measure
3. Convert each of the following angles to degrees by
using π = 3.142. REMEMBER!
(a) 1.8 radian
(b) 4 radian The value of θ must be in radians when applying the
3 formula s = rθ.
(c) 5.16 radian
4. Convert each of the following angles to degrees. 3
3
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(a) π radian
5 Calculate the arc length, s for each of the following
(b) 0.25π radian sectors.
(c) 12 π radian (a) (b)
7 s
s 230º
1.52 rad O
1.2 Arc Length of a Circle O 5.2 cm 2.75 cm

Solution
A Determining arc length, radius and (a) s = rq 1 3.142 2
angle subtended at the centre of a = 5.2 × 1.52 (b) 230° = 230° × 180° rad
circle = 7.904 cm = 4.015 rad
1. Assume a piece of plastic wrapper is cut to wrap s = rq
around a piece of cake that has the shape of sector = 2.75 × 4.015
of a circle. The length of the plastic wrapper cut = 11.04 cm
must be equal to the sum of the arc length, s and Try Questions 1 – 2 in ‘Try This! 1.2’
two times the radius, r.
Example of HOTS
HOTS Question
r
s
Nevis Swing in New Zealand is the biggest canyon
swing in the world with the cable length of 120 m.
r
The length of plastic wrapper = s + 2r A participant can swing up to a maximum angle of
2.5 rad each time the swing is made. Calculate the
maximum distance, in m, of the arc of the swing.
2. It is known that the ratio of the arc length to the
radius of a circle is equal to the angle subtended Solution
s
at the centre of the circle in radian, that is = q. s = rq
r = 120 × 2.5
= 300 m
s
r Try this HOTS Question
θ radian The rope length of a swing at a playground is
1.8 m. Form 5
r

3. By using the equation s r = θ, the following 1.8 m
formula can be derived to find the arc length of a
circle:

For a circle with radius r, the length of arc
subtending the angle θ at the centre of circle Wilson always plays the swing in the evening and
is s = rθ. rides up to 1.4 rad. Calculate the distance, in m,
the arc of the swing.
Answer: 2.52 m

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