Page 36 - Hybrid PBD 2022 Form 5 - Mathematics

Matematik Tingkatan 5 Bab 6 Nisbah dan Graf Fungsi Trigonometri

(c) Rajah di bawah menunjukkan pokok yang (d) Di sebuah makmal sains, lengan robot dengan
baru ditanam oleh Encik Zul di kebunnya. Dia panjang 18 cm seperti yang ditunjukkan dalam
menggunakan dawai berukuran 3 m dan 5 m rajah di bawah diprogramkan untuk bergerak
untuk mengikat batang pokok ke tiang di tanah dari titik B ke titik C. Diberi kos q = −0.656 dan
supaya dapat menyokong pokok itu sementara 0° < q < 180°, hitung sudut q dan jarak, dalam
akarnya memegang tanah dengan kukuh. Diberi cm, di antara titik B dan titik C. TP5
bahawa ∠PQR = 70°. Tentukan nilai bagi TP5 In a science lab, a robotic arm with the length of 18 cm
The diagram shows a tree planted by Mr Zul in his garden. He as shown in the diagram is programmed to move from
uses 3 m and 5 m wires to tie the tree trunk to the stake in the point B to point C. Given cos q = −0.656 and 0° < q < 180°,
ground so that it could support the tree while its roots take calculate the angle q and the distance, in cm, between point
hold. It is given that ∠PQR = 70°. Determine the value of B and point C.
(a) kos y
cos y y
(b) sin x
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C
θ
B x
O
Q 18 cm
5 m x 70° 3 m
y
S P R

PQ PQ kos q = –0.656
(a) kos 70° = cos 70° =
3 3 cos q = –0.656
PQ = 3 kos 70° PQ = 3 cos 70°
= 1.03 m
= 1.03 m Sudut rujukan/Reference angle
= kos 0.656
−1
−1
PS = √SQ – PQ cos 0.656
2
2
= √5 – 1.03 = 49°
2
2
= 4.89 m
q = 180° – 49°
kos y = –kos ∠PSQ = 131°
cos y = –cos ∠PSQ
4.89 α = 180° − 131° C
= – = 49°
5
= – 0.978
sin 49° = AC α 131°
4.89 18 A O 18 cm B
(b) sin x = AC = 18 sin 49°
5 = 13.6 cm
= 0.978
AO AO
kos 49° = cos 49° =
18 18
AO = 18 kos 49° AO = 18 cos 49°
= 11.8 cm = 11.8 cm

AB = 11.8 + 18
= 29.8 cm

BC = √AB + AC
2
2
= √29.8 + 13.6
2
2
= 32.8 cm

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