Latihan Matematika Wajib Kelas X Nilai Rasio Trigonometri Sudut-Sudut Istimewa
# 4
Pilgan

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

A

11010\frac{1}{10}\sqrt{10}

B

21010\frac{2}{10}\sqrt{10}

C

1210\frac{1}{2}\sqrt{10}

D

1510\frac{1}{5}\sqrt{10}

E

3510\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,

sin30°×cos30°×tan30°sin45°×tan45°×cos45°=12×123×133122×1×125\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}}

=112.314.10=\frac{\frac{1}{12}.3}{\frac{1}{4}.\sqrt{10}}

=312104=\frac{\frac{3}{12}}{\frac{\sqrt{10}}{4}}

=312×410=\frac{3}{12}\times\frac{4}{\sqrt{10}}

=121210=\frac{12}{12\sqrt{10}}

=110=\frac{1}{\sqrt{10}}

Rasionalkan.

=110×1010=\frac{1}{\sqrt{10}}\times\frac{\sqrt{10}}{\sqrt{10}}

=11010=\frac{1}{10}\sqrt{10}

Jadi, nilai dari sin30°×cos30°×tan30°sin45°×tan45°×cos45°\frac{\sin30\degree\times\cos30\degree\times\tan30\degree}{\sin45\degree\times\tan45\degree\times\cos45\degree} adalah 11010.\frac{1}{10}\sqrt{10}.