# Transformasi Fungsi Trigonometri

## Konsep Dasar

#### A. Dilatasi vertikal

$$y = A \sin x$$

A = amplitudo

$$y = \sin x, \quad 0^\text{o} \leq x \leq 360^\text{o}$$

Amplitudo  = 1

$$y = 2 \sin x, \quad 0^\text{o} \leq x \leq 360^\text{o}$$

Amplitudo  = 2

$$y = \cos x, \quad 0^\text{o} \leq x \leq 360^\text{o}$$

Amplitudo  = 1

$$y = 2 \cos x, \quad 0^\text{o} \leq x \leq 360^\text{o}$$

Amplitudo  = 2

$$y = \tan x, \quad 0^\text{o} \leq x \leq 360^\text{o}$$

Pada x = 45º, y = 1

$$y = 2 \tan x, \quad 0^\text{o} \leq x \leq 360^\text{o}$$

Pada x = 45º, y = 2

#### B. Dilatasi horizontal

$$y = \sin kx$$

$$\text{Periode} = \dfrac{360}{k}$$

$$y = \sin x, \quad 0^\text{o} \leq x \leq 360^\text{o}$$

Periode = 360º

$$y = \sin 2x, \quad 0^\text{o} \leq x \leq 360^\text{o}$$

Periode = 360º/2 = 180º

$$y = \cos x, \quad 0^\text{o} \leq x \leq 360^\text{o}$$

Periode = 360º

$$y = \cos 2x, \quad 0^\text{o} \leq x \leq 360^\text{o}$$

Periode = 360º/2 = 180º

$$y = \tan x, \quad 0^\text{o} \leq x \leq 360^\text{o}$$

Periode = 180º

$$y = \tan 2x, \quad 0^\text{o} \leq x \leq 180^\text{o}$$

Periode = 180º/2 = 90º

#### C. Translasi Vertikal

$$y = A \sin x + q$$

Kurva bergeser ke arah vertikal sejauh qº

$$y = \sin x, \quad 0^\text{o} \leq x \leq 360^\text{o}$$

$$y = \sin x + 1, \quad 0^\text{o} \leq x \leq 360^\text{o}$$

Kurva bergeser 1 unit ke arah atas

$$y = \cos x, \quad 0^\text{o} \leq x \leq 360^\text{o}$$

$$y = \cos x - 1, \quad 0^\text{o} \leq x \leq 360^\text{o}$$

Kurva bergeser 1 unit ke arah bawah

$$y = \tan x, \quad 0^\text{o} \leq x \leq 360^\text{o}$$

$$y = \tan x + 1, \quad 0^\text{o} \leq x \leq 360^\text{o}$$

Kurva bergeser 1 unit ke arah atas

#### D. Translasi Horizontal

$$y = A \sin (x - p)$$

Kurva bergeser ke arah mendatar sejauh pº

$$y = \sin x, \quad 0^\text{o} \leq x \leq 360^\text{o}$$

$$y = \sin (x - 45^\text{o}) , \quad 0^\text{o} \leq x \leq 360^\text{o}$$

Kurva bergeser 45º ke arah kanan

$$y = \cos x, \quad 0^\text{o} \leq x \leq 360^\text{o}$$

$$y = \cos (x + 45^\text{o}), \quad 0^\text{o} \leq x \leq 360^\text{o}$$

Kurva bergeser 45º ke arah kiri

$$y = \tan x, \quad 0^\text{o} \leq x \leq 360^\text{o}$$

$$y = \tan (x - 45), \quad 0^\text{o} \leq x \leq 360^\text{o}$$

Kurva bergeser 45º ke arah kanan