Page 45 - Hybrid PBD 2022 Form 5 - Mathematics

Matematik Tingkatan 5 Bab 6 Nisbah dan Graf Fungsi Trigonometri

Kertas 2 y
9
1. Dalam rajah di bawah, ABCE ialah sebuah segi
empat tepat dan titik D terletak pada garis lurus 4
EC. x
In the diagram, ABCE is a rectangle and point D lies on the 0 3 6 9 12
straight line EC. Nyatakan fungsi trigonometri bagi graf tersebut
A B dalam bentuk y = a sin bx + c.
State the trigonometric function of the graph in the form of
y = a sin bx + c.
[3 markah / 3 marks]
θ Jawapan / Answer :
E D C
Amplitud/Amplitude = 9 − 4 = 5, jadi/therefore, a = 5
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360
Diberi DC = 5 cm dan AE = 4 cm, cari nilai Tempoh/Period = 12, jadi/therefore, b = 12
kos q. b = 30
Given that DC = 5 cm and AE = 4 cm, find the value of cos q. Graf beranjak 4 unit ke atas, jadi c = 4
[3 markah / 3 marks] Graph moves 4 units up, therefore
Jawapan / Answer : Maka/Hence, y = 5 sin 30x + 4
AD = DC = 5 cm
2
ED = √5 – 4 = 3 cm 4. Jadual di bawah menunjukkan ketinggian
2
kos q = −kos ∠ADE kedudukan Abu dari tanah ketika dia menaiki
cos q = −cos ∠ADE roda pemerhatian. KBAT Mengaplikasi
ED The table shows the height of Abu’s position from the ground as
= – he rides on an observation wheel.
AD
3 Masa (minit)
= – 0 8 16 24 32
5 Time (minutes)
Ketinggian (m) 90 165 90 15 90
2. Lakar graf bagi y = 2 sin x + 1 untuk 0° < x < 360°. Height (m)
Kemudian, lakar pada paksi-paksi yang sama, (a) Berdasarkan jadual, nyatakan jenis fungsi
graf bagi y = 2 sin 2x + 1 untuk 0° < x < 360°. trigonometri.
Seterusnya, nyatakan bilangan titik persilangan Based on the table, state the type of trigonometric
kedua-dua graf tersebut. function.
Sketch the graph of y = 2 sin x + 1 for 0° < x < 360°. Then, [1 markah / 1 mark]
sketch on the same axes, the graph of y = 2 sin 2x + 1 for (b) Jika y ialah ketinggian kedudukan Abu dari
0° < x < 360°. Hence, determine the number of intersection tanah (m) dan x ialah masa (minit), lakarkan
points between both graphs. graf dan nyatakan fungsi trigonometri.
[5 markah / 5 marks] If y is the height of Abu’s position from the ground (m)
Jawapan / Answer : and x is the time (minutes), sketch the graph and state
the trigonometric function.
y [5 markah / 5 marks]
y = 2 sin x + 1
KBAT
3 Tip KBATKBAT
y = 2 sin 2x + 1
Perhatikan data bagi jadual.
1 Observe the data of the table.
x
0 180° 360° Jawapan / Answer :
(a) sinus / sine
Bilangan titik persilangan = 5 (b) y
Number of intersection points 165

3. Graf berikut mewakili paras air di sungai semasa 90
hari hujan yang diukur dengan pemancar tahap 15
apungan. Diberi bahawa y mewakili paras air,
dalam m, dan x mewakili masa, dalam jam. 0 8 16 24 32 x
The graph illustrates the water level in a river during a heavy y = a sin bx + c
down pour measured with a float level transmitter. It is given
that y represents the water level, in m, and x represents time, a = 165 – 15 = 75
in hours. 2

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