Persamaan Trigonometri

5√3 sin x - 5 cos x - 5√3 = 0

sederhanakan → bagi 5

√3 sin x - cos x = √3

h cos (x - a) = √3

•

m cos x + n sin x = h cos (x - a)

√3 sin x - cos x = √3

h = √(m² + n²)

h = √((-1)² + (√3)²)

h = 2

(m,n) = (-1,√3) → kuadran II

a = arc tan (n/m)

a = arc tan (√3 / -1)

a = 120°

√3 sin x - cos x = √3

2 cos (x - 120°) = √3

cos (x - 120°) = 1/2 √3

• x - 120° = 30° + k.360°

x = 150° + k.360° ... (1)

• x - 120° = -30° + k.360°

x = 90° + k.360° ... (2)

k bilangan bulat

k = 0 → x = {90° , 150°}

dan seterusnya

Interval 0° ≤ x ≤ 360°

HP = {90° , 150°}