Page 57 - Focus SPM 2022 - Additional Mathematics

Additional Mathematics SPM Chapter 1 Circular Measure

2
Solution
Convert 3.142
1
(a) 1.2 radian to degree by using π = 3.142, (a) 35° = 35° × 180° 2 rad
(b) 7 π radian to degree without using π = 3.142. = 0.6109 rad
4
Let change in speed = v
Solution v = (60 – 20) km h –1
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180 °
1
(a) 1.2 rad = 1.2 × 3.142 2 1 rad 0.6109 rad
–1
= 68.75° v = 65.48 km h for 1 radian
1
Minion Pro 10pt = — (b) Change in speed = 65.48 km h –1 × 1.8 rad
2 C C A L C U L A T O R Corner 1 rad
C
---------------------------------------- = 117.9 km h –1
Arial 8.5pt = 1 The following type of calculator can be used to convert the
angle 1.2 radian to an angle in degree:
2
---------------------------------------- Try this HOTS Question
Casio FX-570MS: Press MODE 4 times, choose 1 ,
Cth KBAT_Optima 9pt = 80 press 1 . 2 , SHIFT , Ans , choose 2 , press = . The diagram below shows the speedometer used to
measure the speed of a car in kilometre per hour.
1.25
---------------------------------------- Casio FX-570ES: Press SHIFT , SETUP , choose 3 ,
press 1 . 2 , SHIFT , Ans , choose 2 , press = .
---------------------------------------- 100 120 140 160 180 200
80 220 240 260
60
2
280
(b) 7 π rad = 1 7 π × 180 ° 40 20 300
4 4 π 0 km/h 320
= 315°
–1
Try Questions 3 - 4 in ‘Try This! 1.1’ It is given that the angle between 60 km h and
120 km h is 45°.
–1
(a) Calculate the change in speed, in km h , that
–1
Example of HOTS is represented by 1 radian.
HOTS Question
(b) If the pointer of the speedometer changes by
The diagram below shows the speedometer used to 2.1 radians, what is the change in speed, in
measure the speed of a motorcycle in kilometre per –1
hour. km h , experienced by the car?
[Use π = 3.142]
Answer:
120 140 160 –1
100 180 (a) 76.38 km h
80 200
60 220
40 240 (b) 160.4 km h –1
20 260
0 280
It is given that the angle between 20 km h and Try This! 1.1
–1
Form 5
60 km h is 35°.
–1
(a) Calculate the change in speed, in km h , that is 1. Convert each of the following angles to radians in
–1
represented by 1 radian. terms of π.
(a) 95°
(b) If the pointer of the speedometer changes by 1.8
radians, what is the change in speed, in km h , (b) 22.5°
–1
(c) 56°15’
experienced by the motorcycle?
2. Convert each of the following angles to radians by
[Use π = 3.142]
using π = 3.142.
(a) 121°
(b) 50.72°
(c) 82°2’
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