Trigonometri

​TRIGONOMETRY

​KELAS 12
DISUSUN OLEH :
SRI RAHAYU

​PART 1

​History of Trigonometry

Trigonometry is a branch of mathematics that studies relationships that include the length and angle of triangles. This field arose in the 3rd century BC from the use of geometry to study astronomy. Trigonometry in Greek itself means a measure in a triangle. This concept was first discovered by an astronomer and mathematician from Khorasan, Persia named Al Marwazi, or more fully named Ahmad ibn 'Abdallah Habash Hasib Marwazi.

​Trigonometric Concepts

Al Marwazi succeeded in explaining the trigonometric ratios of sine (sin), cosine (cos), tangent (tan) and cotangen (cot). Through this concept, many things can finally be learned, such as in the fields of astronomy, electronics, statistics, chemistry, economics, even to music and acoustics.

For example, in the field of astronomy, we can do research on solar eclipses, like what Al Marwazi himself did in 829. He conducted research by making examples of the determination of the time and height of the sun.

In addition, trigonometry is also useful in various other fields, we can measure the height of mountains without having to climb it, or measure the width of rivers without having to pass through it first.

RUMUS FUNGSI TRIGONOMETRI

Sudut- sudut istimewa

Multiple Choice

Besar sudut $$45\degree\ adalah\ ...$$

• 1

• $$\frac{1}{2}$$

• $$\frac{1}{2}\sqrt[]{3}$$

• $$0$$

Contoh soal

​Sebuah segitiga siku-siku diketahui memiliki sisi alas (a) 6 cm dan sisi miring (c) 10 cm. Hitung dengan rumus Pythagoras tinggi (b) dari segitiga siku-siku ini.

​Jawab :

Diketahui : a = 6cm

c = 10cm

Ditanya : b....?

Multiple Choice

Tentukan nilai cos pada segitiga di samping adalah ...

• $$\frac{x}{r}$$

• $$\frac{y}{r}$$

• $$\frac{r}{x}$$

• $$\frac{x}{y}$$

Multiple Choice

Diketahui tan $$\alpha\ =\frac{4}{3}$$ , maka pernyataan yang tepat di bawah ini adalah ...

• $$\sin\ \alpha=\frac{2}{3}$$

• $$\sin\ \alpha=\frac{3}{4}$$

• sin $$\alpha=\frac{3}{5}$$

• tan 3 $$\alpha=\frac{3}{5}$$