Page 40 - Hybrid PBD 2022 Form 5 - Mathematics

Matematik Tingkatan 5 Bab 6 Nisbah dan Graf Fungsi Trigonometri
11. Lakar graf bagi fungsi yang diberikan dan nyatakan nilai maksimum dan nilai minimum. SP 6.2.1 TP4
Sketch the graph of the given functions and state the maximum and minimum values.

(a) y = kos x untuk 90° < x < 360° (b) y = tan x untuk / for
y = sin x untuk/for 90° < x < 270° y = cos x for 90° < x < 360° 90° < x < 270°

y y y

1 1
x x
0 90° 180° 270° 0 90° 180° 270° 360° x
–1 –1 0 90° 180° 270°

Nilai maksimum = 1 Nilai maksimum = 1 Tiada nilai maksimum dan
Maximum value Maximum value nilai minimum
Nilai minimum = −1 Nilai minimum = −1 No maximum value and minimum
Minimum value Minimum value value

FOKUS TOPIK

1. Tempoh
Period

Amplitud dan Tempoh
Amplitud Penerbitan Pelangi Sdn Bhd. All Rights Reserved
Amplitude Amplitude and Period
INFO

2. Kesan perubahan pemalar a, b dan c bagi y = a sin bx + c, y = a kos bx + c dan y = a tan bx + c, a . 0, b . 0
The effects of changes in constants a, b, and c on y = a sin bx + c, y = a cos bx + c and y = a tan bx + c, a . 0, b . 0
(a) Nilai a berubah:
The value of a changes:
➢ Bagi y = a sin bx + c dan y = a kos bx + c, amplitude fungsi = a
For y = a sin bx + c and y = a cos bx + c, amplitude of function = a
➢ Bagi y = a tan bx + c, lengkung graf berubah dan tiada amplitud
For y = a tan bx + c, graph curvature changes and there is no amplitude

(b) Nilai b berubah:
The value of b changes:
➢ Graf kelihatan mampat secara mengufuk apabila nilai b bertambah dan tempoh fungsi semakin berkurang
The graph appears to compress horizontally when the value of b increases and the period of the function decreases
360° 180°
➢ Tempoh fungsi sinus and kosinus = b ; Tempoh fungsi tangen = b
360° 180°
Period of sine and cosine functions = ; Period of tangent function =
b b
(c) Nilai c berubah:
The value of c changes:
➢ Apabila c . 0, graf beranjak c unit secara menegak ke atas
When c . 0, the graph moves c units vertically up
➢ Apabila c , 0, graf beranjak c unit secara menegak ke bawah
When c , 0, the graph moves c units vertically down

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