Jawab:

Penjelasan dengan langkah-langkah:

1a. Sin 120 = Sin (180 - 60) = Sin 60 = √3/2

b. Cos 330 = Cos (360 - 30) = Cos 30 = √3/2

2. A(10, 60°) ⇒ r = 10; α = 60°

x = 10 cos 60° = 10 (1/2) = 5

y = 10 sin 60° = 10 (√3/2) = 5√3

A(10, 60°) ⇒ A(5, 5√3)

3. P(3, 3√3) ⇒ x = 3; y = 3√3

r² = 3² + (3√3)² = 9 + 27 = 36

r = √36 = 6

tan α = y/x = 3√3/3 = √3

α = arc tan √3 = 60°

P(3, 3√3) ⇒ P(6, 60°)

4. Luas = 1/2 x AB x BC x Sin ABC

            = 1/2 x 9 x 12 x Sin 30°

            = 54 x 1/2

            = 27

5. AC/Sin ABC = BC/Sin BAC

4/Sin 60 = BC/Sin 30

4/(√3/2) = BC/(1/2)

8/√3 = 2BC

BC = 8/√3 : 2 = 4/√3

6. AC² = AB² + BC² - 2(AB)(BC)(Cos B)

AC² = 5² + 7² - 2(5)(7)(Cos 60)

AC² = 25 + 49 - 70(1/2)

AC² = 25 + 49 - 35

AC² = 39

AC = √39 = 6.245