Grafik Fungsi Trigonometri

Grafik	Keterangan
$y = \sin x, 0^{o} \leq x \leq 360^{o}$	Periode = $360^{o}$ Amplitudo = 1 $y_{max} = 1$ $y_{min} = - 1$
$y = 2 \sin x, 0^{o} \leq x \leq 360^{o}$	Kurva diperbesar 2 kali dalam arah Y Periode = $360^{o}$ Amplitudo = 2 $y_{max} = 2$ $y_{min} = - 2$
$y = \sin 2 x, 0^{o} \leq x \leq 360^{o}$	Kurva diperkecil $\frac{1}{2}$ kali dalam arah X Periode = $\frac{360^{o}}{2} = 180^{o}$ Amplitudo = 1 $y_{max} = 1$ $y_{min} = - 1$
$y = \sin x + 1, 0^{o} \leq x \leq 360^{o}$	Kurva bergeser 1 unit ke atas Periode = $360^{o}$ Amplitudo = 1 $y_{max} = 2$ $y_{min} = 0$
$y = \sin x - 1, 0^{o} \leq x \leq 360^{o}$	Kurva bergeser 1 unit ke bawah Periode = $360^{o}$ Amplitudo = 1 $y_{max} = 0$ $y_{min} = - 2$
$y = \sin (x - 45^{o}), 0^{o} \leq x \leq 360^{o}$	Kurva bergeser 45º ke kanan Periode = $360^{o}$ Amplitudo = 1 $y_{max} = 1$ $y_{min} = - 1$
$y = \sin (x + 45^{o}), 0^{o} \leq x \leq 360^{o}$	Kurva bergeser 45º ke kiri Periode = $360^{o}$ Amplitudo = 1 $y_{max} = 1$ $y_{min} = - 1$

Grafik

Keterangan

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

Rendered by QuickLaTeX.com

Periode =

360^{o}

Amplitudo = 1

$y_{max} = 1$

$y_{min} = - 1$

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

Rendered by QuickLaTeX.com

Kurva diperbesar 2 kali dalam arah Y

Periode = $360^{o}$

Amplitudo = 2

$y_{max} = 2$

$y_{min} = - 2$

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

Rendered by QuickLaTeX.com

Kurva diperkecil

\frac{1}{2}

kali dalam arah X

Periode = $\frac{360^{o}}{2} = 180^{o}$

Amplitudo = 1

$y_{max} = 1$

$y_{min} = - 1$

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

Rendered by QuickLaTeX.com

Kurva bergeser 1 unit ke atas

Periode = $360^{o}$

Amplitudo = 1

$y_{max} = 2$

$y_{min} = 0$

y = \sin x - 1, 0^{o} \leq x \leq 360^{o}

Rendered by QuickLaTeX.com

Kurva bergeser 1 unit ke bawah

Periode = $360^{o}$

Amplitudo = 1

$y_{max} = 0$

$y_{min} = - 2$

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

Rendered by QuickLaTeX.com

Kurva bergeser 45º ke kanan

Periode = $360^{o}$

Amplitudo = 1

$y_{max} = 1$

$y_{min} = - 1$

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

Rendered by QuickLaTeX.com

Kurva bergeser 45º ke kiri

Periode = $360^{o}$

Amplitudo = 1

$y_{max} = 1$

$y_{min} = - 1$

Grafik	Keterangan
$y = \cos x, 0^{o} \leq x \leq 360^{o}$	Periode = $360^{o}$ Amplitudo = 1 $y_{max} = 1$ $y_{min} = - 1$
$y = 2 \cos x, 0^{o} \leq x \leq 360^{o}$	Kurva diperbesar 2 kali dalam arah Y Periode = $360^{o}$ Amplitudo = 2 $y_{max} = 2$ $y_{min} = - 2$
$y = \cos 2 x, 0^{o} \leq x \leq 360^{o}$	Kurva diperkecil $\frac{1}{2}$ kali dalam arah X Periode = $\frac{360^{o}}{2} = 180^{o}$ Amplitudo = 1 $y_{max} = 1$ $y_{min} = - 1$
$y = \cos x + 1, 0^{o} \leq x \leq 360^{o}$	Kurva bergeser 1 unit ke atas Periode = $360^{o}$ Amplitudo = 1 $y_{max} = 2$ $y_{min} = 0$
$y = \cos x - 1, 0^{o} \leq x \leq 360^{o}$	Kurva bergeser 1 unit ke bawah Periode = $360^{o}$ Amplitudo = 1 $y_{max} = 0$ $y_{min} = - 2$
$y = \cos (x - 45^{o}), 0^{o} \leq x \leq 360^{o}$	Kurva bergeser 45º ke kanan Periode = $360^{o}$ Amplitudo = 1 $y_{max} = 1$ $y_{min} = - 1$
$y = \cos (x + 45^{o}), 0^{o} \leq x \leq 360^{o}$	Kurva bergeser 45º ke kiri Periode = $360^{o}$ Amplitudo = 1 $y_{max} = 1$ $y_{min} = - 1$

Grafik

Keterangan

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

Rendered by QuickLaTeX.com

Periode =

360^{o}

Amplitudo = 1

$y_{max} = 1$

$y_{min} = - 1$

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

Rendered by QuickLaTeX.com

Kurva diperbesar 2 kali dalam arah Y

Periode = $360^{o}$

Amplitudo = 2

$y_{max} = 2$

$y_{min} = - 2$

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

Rendered by QuickLaTeX.com

Kurva diperkecil

\frac{1}{2}

kali dalam arah X

Periode = $\frac{360^{o}}{2} = 180^{o}$

Amplitudo = 1

$y_{max} = 1$

$y_{min} = - 1$

y = \cos x + 1, 0^{o} \leq x \leq 360^{o}

Rendered by QuickLaTeX.com

Kurva bergeser 1 unit ke atas

Periode = $360^{o}$

Amplitudo = 1

$y_{max} = 2$

$y_{min} = 0$

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

Rendered by QuickLaTeX.com

Kurva bergeser 1 unit ke bawah

Periode = $360^{o}$

Amplitudo = 1

$y_{max} = 0$

$y_{min} = - 2$

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

Rendered by QuickLaTeX.com

Kurva bergeser 45º ke kanan

Periode = $360^{o}$

Amplitudo = 1

$y_{max} = 1$

$y_{min} = - 1$

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

Rendered by QuickLaTeX.com

Kurva bergeser 45º ke kiri

Periode = $360^{o}$

Amplitudo = 1

$y_{max} = 1$

$y_{min} = - 1$

Grafik	Keterangan
$y = \tan x, 0^{o} \leq x \leq 360^{o}$	Periode = $180^{o}$ Pada x = 45º, y = 1
$y = 2 \tan x, 0^{o} \leq x \leq 360^{o}$	Periode = $180^{o}$ Pada x = 45º, y = 2
$y = \tan 2 x, 0^{o} \leq x \leq 180^{o}$	Periode = $\frac{180^{o}}{2} = 90^{o}$ Pada x = 22.5º, y = 1
$y = \tan x + 1, 0^{o} \leq x \leq 360^{o}$	Kurva bergeser 1 unit ke atas Periode = $180^{o}$ Pada x = 45º, y = 2
$y = \tan x - 1, 0^{o} \leq x \leq 360^{o}$	Kurva bergeser 1 unit ke bawah Periode = $180^{o}$ Pada x = 45º, y = 0
$y = \tan (x - 45), 0^{o} \leq x \leq 360^{o}$	Kurva bergeser 45º ke kanan Periode = $180^{o}$ Pada x = 90º, y = 1
$y = \tan (x + 45), 0^{o} \leq x \leq 360^{o}$	Kurva bergeser 45º ke kiri Periode = $180^{o}$ Pada x = 0º, y = 1

Grafik

Keterangan

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

Rendered by QuickLaTeX.com

Periode =

180^{o}

Pada x = 45º, y = 1

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

Rendered by QuickLaTeX.com

Periode =

180^{o}

Pada x = 45º, y = 2

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

Rendered by QuickLaTeX.com

Periode =

\frac{180^{o}}{2} = 90^{o}

Pada x = 22.5º, y = 1

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

Rendered by QuickLaTeX.com

Kurva bergeser 1 unit ke atas

Periode = $180^{o}$

Pada x = 45º, y = 2

y = \tan x - 1, 0^{o} \leq x \leq 360^{o}

Rendered by QuickLaTeX.com

Kurva bergeser 1 unit ke bawah

Periode = $180^{o}$

Pada x = 45º, y = 0

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

Rendered by QuickLaTeX.com

Kurva bergeser 45º ke kanan

Periode = $180^{o}$

Pada x = 90º, y = 1

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

Rendered by QuickLaTeX.com

Kurva bergeser 45º ke kiri

Periode = $180^{o}$

Pada x = 0º, y = 1

SOAL LATIHAN

Sketsa grafik $y = 3 \sin (2 x + 60^{o}) - 1$ , $0^{o} \leq x \leq 360^{o}$ dan kemudian tentukan:

(A) Amplitudo

(B) Periode

Pembahasan:

Sketsa grafik $y = 1 - 2 \sin (3 x - \frac{1}{2} π)$ , $0 \leq x \leq 2 π$ dan kemudian tentukan:

(A) Amplitudo

(B) Periode

Pembahasan: