Page 60 - Focus SPM 2022 - Additional Mathematics

Additional Mathematics SPM Chapter 1 Circular Measure

p = 2r sin q Perimeter of the shaded segment
2 = s + p
= 2 × 3.9 × sin 1 1.42 2 = 2.895 + 2.822
2
= 2 × 3.9 × sin 0.71 = 5.717 cm
= 5.084 cm
Try Questions 6 - 7 in ‘Try This! 1.2’
Perimeter of the shaded segment
= s + p
= 5.538 + 5.084 7
= 10.62 cm The diagram below shows a sector OFGH with radius
10 cm. It is given that the length of chord FH = 18 cm.
Alternative Method Calculate the perimeter, in cm, of the shaded region
Sine rule: FGH.
a = b
sin A sin B F G
p = 3.9 10 cm 18 cm
sin 1.42 3.142 – 1.42
sin 1 2 2 O H

p = 3.9 × sin 1.42 Solution
sin 0.861
= 5.083 cm For ∆OFH,
18 = 10 + 10 – 2(10)(10)(cos ∠FOH)
2
2
2
Cosine rule: 2 2 2
a = b + c – 2bc cos A cos ∠FOH = 10 + 10 – 18
2
2
2
p = (3.9) + (3.9) – (2)(3.9)(3.9)(cos 1.42) 2(10)(10)
2
2
2

= –0.62
p = 5.084 cm
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∠FOH = cos (–0.62)
–1
C
C C A L C U L A T O R Corner = 2.2395 rad
s = rq
The following type of calculator can be used to calculate = 10 × 2.2395
sin 0.71 radian.
= 22.395 cm
Casio FX-570MS: Press MODE 4 times, choose 2 ,
press sin 0 . 7 1 = Perimeter of the shaded segment
Casio FX-570ES: Press SHIFT , SETUP , choose 4 , = s + p
press sin 0 . 7 1 = = 22.395 + 18
= 40.395 cm
1
(b) 44.7° = 44.7° × 3.142 2 rad Try Question 8 in ‘Try This! 1.2’ Form 5
180°
= 0.7803 rad
s = rq C C A L C U L A T O R Corner
C
= 3.71 × 0.7803
= 2.895 cm The following type of calculator can be used to calculate
cos (–0.62):
−1
p = 2r sin q
2 Casio FX-570MS: Press MODE 4 times, choose 2 ,
= 2 × 3.71 × sin 1 44.7° 2 press SHIFT cos – 0 . 6 2 =
2
= 2 × 3.71 × sin 22.35° Casio FX-570ES: Press SHIFT , SETUP , choose 4 ,
= 2.822 cm press SHIFT cos – 0 . 6 2 =
221