Question

1. Tentukan HP dari persamaan berikut :

2√3 sin x - 2 cos x = 2√3 ; 0°≤x≤360°

Answer 1

Trigonometri

2√3 sin x - 2 cos x = 2√3

sin (+), cos (-) → kuadran 2

K = √((2√3)² + (-2)²) = 4

tan a = (2√3 / (-2)) = - √3

a = 120°

2√3 sin x - 2 cos x = 2√3

K cos (x - a) = 2√3

cos (x - 120°) = 2√3 /4

cos (x - 120°) = 1/2 √3

x - 120° = 30° + k.360°

x = 150° + k.360°

cos (x - 120°) = 1/2 √3

x - 120° = 330° + k.360°

x = 450° + k.360°

x = 90° + k.360°

k bilangan bulat

0° ≤ x ≤ 360°

k = 0 → x = 90° atau x = 150°

HP = {90°, 150°}