Page 5 - 1202 Question Bank Additional Mathematics Form 5

1 Circular Measure
Chapter

NOTES

1.1 Radian (a) —–— = —–— = —–————–——–
θ rad
Arc length, s
θ °
2πr (Circumference)
360°
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2π
1. One radian is the measure of an angle subtended (b) Arc length AB, s = rθ
at the centre O of a circle where the arc length, s (c) Length of chord AB:
is the same as the radius of the circle, r, that is, (i) AB = r + r – 2r cos θ ° (Cosine rule)
2
2
2
2
s = r = 1 rad. r
AB
(ii) ——– = ————––— (Sine rule)
180° – θ °

A sin θ ° sin ———–– 2
r 2
s
1 rad
O 1.3 Area of Sector of a Circle
B
1. Given a circle with centre O and a radius of r units
where ∠AOB = θ rad (or θ °), then
2. 360° = 2π rad A
r
1.2 Arc Length of a Circle
O θ
1. Given a circle with centre O and a radius of r units
where ∠AOB = θ rad (or θ °) and the arc length AB is B
s units, then
A θ ° θ rad Area of the sector
(a) —–— = —–— = —–————–—–—––
2
r 360° 2π πr (Area of the circle)
s 1 2
θ (b) Area of sector AOB = —r θ
O 2
(c) Area of the shaded segment
B = Area of the sector AOB – Area of triangle AOB
1 1
= —r θ – —r sin θ °
2
2
2 2
PAPER 1

Section A

1. The perimeter of a sector AOB of a circle with centre Answer:
SPM O and an arc length of 5.4 cm is 23.4 cm. Find (a)
CLONE
(a) the radius of the circle, [3 marks]
(b) the angle AOB subtended at the centre of the
circle. [2 marks] (b)

PB Question 1: 1
SOS TIP PBPB (a) Perimeter of a sector = r + r + Arc length 1 SOS TIP

(b) Use s = rθ

01_1202 QB AMath F5.indd 1 02/12/2021 8:44 PM