Transformasi Fungsi Trigonometri

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

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

Amplitudo  = 2

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

Amplitudo  = 1

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

Amplitudo  = 2

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

Pada x = 45º, y = 1

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

Pada x = 45º, y = 2

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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

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

Periode = 360º/2 = 180º

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

Periode = 360º

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

Periode = 360º/2 = 180º

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

Periode = 180º

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

Periode = 180º/2 = 90º

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C. Translasi Vertikal

\(y = A \sin x + q\)

Kurva bergeser ke arah vertikal sejauh qº


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

 

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

Kurva bergeser 1 unit ke arah atas

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

 

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

Kurva bergeser 1 unit ke arah bawah

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

 

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

Kurva bergeser 1 unit ke arah atas

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D. Translasi Horizontal

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

Kurva bergeser ke arah mendatar sejauh pº


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

 

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

Kurva bergeser 45º ke arah kanan

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

 

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

Kurva bergeser 45º ke arah kiri

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

 

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

Kurva bergeser 45º ke arah kanan

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Kembali ke Transformasi Fungsi Trigonometri

Transformasi Fungsi Trigonometri