Bank Soal Matematika SMA Nilai Rasio Trigonometri Sudut-Sudut Istimewa

Soal

Pilgan

Lihat Pembahasan

Nilai dari $\frac{\sin30\degree\times\cos30\degree\times\tan30\degree}{\sin45\degree\times\tan45\degree\times\cos45\degree}=....$

E

$\frac{3}{5}\sqrt{10}$

Pembahasan:

Perhatikan tabel di bawah ini!

Tabel di atas menunjukkan nilai-nilai sinus, cosinus, dan tangen sudut-sudut istimewa.

Sehingga,

$\frac{\sin30\degree\times\cos30\degree\times\tan30\degree}{\sin45\degree\times\tan45\degree\times\cos45\degree}=\frac{\frac{1}{2}\times\frac{1}{2}\sqrt{3}\times\frac{1}{3}\sqrt{3}}{\frac{1}{2}\sqrt{2}\times1\times\frac{1}{2}\sqrt{5}}$

$=\frac{\frac{1}{12}.3}{\frac{1}{4}.\sqrt{10}}$

$=\frac{\frac{3}{12}}{\frac{\sqrt{10}}{4}}$

$=\frac{3}{12}\times\frac{4}{\sqrt{10}}$

$=\frac{12}{12\sqrt{10}}$

$=\frac{1}{\sqrt{10}}$

Rasionalkan.

$=\frac{1}{\sqrt{10}}\times\frac{\sqrt{10}}{\sqrt{10}}$

$=\frac{1}{10}\sqrt{10}$

Jadi, nilai dari $\frac{\sin30\degree\times\cos30\degree\times\tan30\degree}{\sin45\degree\times\tan45\degree\times\cos45\degree}$ adalah $\frac{1}{10}\sqrt{10}.$