Page 46 - Hybrid PBD 2022 Form 5 - Mathematics

Matematik Tingkatan 5 Bab 6 Nisbah dan Graf Fungsi Trigonometri
360 45 (b) Rajah di bawah menunjukkan kincir angin
b = =
32 4 dengan 3 bilah yang sama panjang, iaitu
c = 90 OA = OB = OC. Diberi bahawa sin q = −0.5,
45 PC = 1 m dan ∠OPC ialah 90°.
Maka / Hence, y = 75 sin x + 90 The diagram shows a windmill consisting of 3 blades
4
with equal length, that is OA = OB = OC. It is given that
sin q = −0.5, PC = 1 m and ∠OPC is 90°.
5. (a) Graf di bawah menunjukkan gelombang B
bunyi dari mikrofon dengan y = a kos bx + c
yang mewakili voltan dan x ialah masa dalam
milisaat. θ
The graph shows the sound wave from a microphone P
with y = a cos bx + c that represents the voltage and x is O
the time in milliseconds. 1 m
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C A
Voltan (volt)
Voltage (volts)
20
16
12
(i) Berdasarkan rajah, hitung nilai bagi q.
Based on the diagram, calculate the value of q.
(ii) Tentukan sama ada putaran bilah-bilah
Masa (milisaat)
0 30 60 90 120 150 180 Time (milliseconds) tersebut membentuk satu bulatan unit.
(i) Tentukan nilai bagi a, b dan c. Determine whether the rotation of the blades forms
a unit circle.
Determine the values of a, b and c.
(ii) Nyatakan masa semasa voltan adalah [4 markah / 4 marks]
maksimum. Jawapan / Answer :
State the time that gives the maximum voltage. (b) (i) sin q = −0.5
[4 markah / 4 marks] q terletak di sukuan III.
Jawapan / Answer : q is located in quadrant III.
(a) (i) y = a kos bx + c Sudut rujukan / Reference angle
20 – 12 −1
Amplitud / Amplitude = = sin 0.5
2 = 30°
= 4
Jadi / Therefore, a = 4 q = 180° + 30°
360 = 210°
b =
60 PC P O
= 6 (ii) sin 30° = OC 30°
c = 20 − 4 (atau/or 12 + 4) 1 m
= 16 0.5 = 1
OC
(ii) Voltage adalah maksimum semasa OC = 2 m C
x = 0 milisaat, 60 milisaat, 120 milisaat Oleh sebab panjang bilah kincir angin
dan 180 milisaat. ialah 2 m, maka putarannya tidak akan
Voltage is maximum when x = 0 millisecond,
60 milliseconds, 120 milliseconds and 180 membentuk bulatan unit.
milliseconds. Since the length of the blade is 2 m, the rotation of
the blades does not form a unit circle.

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