Perbandingan Trigonometri Pada Segitiga Siku-siku

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$\sin α = \frac{y}{r} = \frac{depan}{miring}$

$\cos α = \frac{x}{r} = \frac{samping}{miring}$

$\tan α = \frac{y}{x} = \frac{depan}{samping}$

$\sec α = \frac{1}{\cos α}$

$\csc α = \frac{1}{\sin α}$

$\cot α = \frac{1}{\tan α}$

	$0$	$30^{o}$	$45^{o}$	$60^{o}$	$90^{o}$	$37^{o}$	$53^{o}$
Sin	0	$\frac{1}{2}$	$\frac{1}{2} \sqrt{2}$	$\frac{1}{2} \sqrt{3}$	1	$0, 6$	$0, 8$
Cos	1	$\frac{1}{2} \sqrt{3}$	$\frac{1}{2} \sqrt{2}$	$\frac{1}{2}$	0	$0, 8$	$0, 6$
Tan	0	$\frac{1}{3} \sqrt{3}$	1	$\sqrt{3}$	∼	$\frac{3}{4}$	$\frac{4}{3}$

Contoh 01

Diketahui segitiga siku-siku di bawah ini:

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Tentukan nilai dari $\sin α$ , $\cos α$ dan $\tan α$

Menentukan nilai r

$\begin{aligned} x^{2} + 5^{2} & = r^{2} \\ 3^{2} + 4^{2} & = r^{2} \\ 9 + 16 & = r^{2} \\ 25 & = r^{2} \\ r & = \pm 5 \end{aligned}$

Gunakan nilai positif untuk $r = 5$

$\sin α = \frac{depan}{miring} = \frac{4}{5}$

$\cos α = \frac{samping}{miring} = \frac{3}{5}$

$\tan α = \frac{depan}{samping} = \frac{4}{3}$

Contoh 02

Pada sebuah segitiga siku-siku ABC, diketahui nilai dari $\sin A = \frac{5}{13}$ .

Tentukan nilai dari $\cos A$ dan $\tan A$

$\sin A = \frac{y}{r} = \frac{depan}{miring} = \frac{5}{13}$

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Menentukan nilai $x$

$\begin{aligned} x^{2} + 5^{2} & = 13^{2} \\ x^{2} + 25 & = 169 \\ x^{2} & = 144 \\ x & = \pm 12 \end{aligned}$

Karena panjang AB harus bernilai positif, maka $x = 12$

$\cos A = \frac{x}{r} = \frac{samping}{miring} = \frac{12}{13}$

$\tan A = \frac{y}{x} = \frac{depan}{samping} = \frac{5}{12}$