Page 59 - Focus SPM 2022 - Additional Mathematics

Additional Mathematics SPM Chapter 1 Circular Measure

4 B Determining perimeter of segment
of a circle
Calculate the radius, r, for each of the following sectors.
(a) 1. Observe that the shaded region which is known
as the segment of the circle is surrounded by arc
4.8 rad s and chord p.
r O
15.15 cm
s
r p
θ
(b) O
7.1 cm
1
Minion Pro 10pt = —
2 89.6º
---------------------------------------- O r 2. For a circle with radius r, the chord length
Arial 8.5pt = 1 subtending the angle θ at the centre of the circle
2
---------------------------------------- Solution is p = 2r sin .
q
Cth KBAT_Optima 9pt = 80 (a) r = s 2 q
1.25
---------------------------------------- q 3. By using s = rq and p = 2r sin , the following
2
= 15.15 formula can be derived to determine the
---------------------------------------- 4.8 perimeter of segment of a circle.
= 3.156 cm
Perimeter of segment of a circle
1
(b) 89.6° = 89.6° × 3.142 2 rad = arc length, s + chord length, p
q
180°
= rθ + 2r sin
= 1.564 rad 2
1 q = Penerbitan Pelangi Sdn Bhd. All Rights Reserved.
s
r =
XX q REMEMBER!
7.1
Penyelesaian = 1.564 Solution of triangle in circular measures can involve the
(a) XX use of sine rule and cosine rule, that is
= 4.540 cm a b
Sine rule : =
sin A sin B
Try Questions 3 - 4 in ‘Try This! 1.2’ Cosine rule : a = b + c – 2bc cos A
2
2
2
5
Calculate the angle θ, in radian, for sector AOB in the 6
diagram below. Calculate the perimeter, in cm, of the shaded segment
of each of the following circles.
7.1 cm
A [Use π = 3.142].
Form 5
θ B (a) (b)
O 4 cm 1.42 rad
O
Solution O
s 3.9 cm 44.7º 3.71 cm
r

= 7.1 Solution
4 (a) s = rq
= 1.775 rad = 3.9 × 1.42
= 5.538 cm
Try Question 5 in ‘Try This! 1.2’

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