Question

Himpunan penyelesaian
Sin x - √3 cos x = -1 adalah

A. {0°, 120°}
B. {90° , 330°}
C. {60° , 180°}
D. {90° , 120°}
E. {30° , 270°}

Answer 1

Verified answer

TriGonoMetRi

a sin x + b cos x = k cos (x - θ)
k = √(a² + b²)

tan θ = a/b

•••
sin x - √3 cos x = -1
k = √(1² + (-√3)²) = 2
tan θ = 1/-√3 ---> θ = 150°

2 cos (x - 150°) = -1
cos (x - 150°) = -1/2
x - 150° = 120° ---> x = 270°
x - 150° = 240° ---> x = 390° = 30°

Jawab : E