Question

Himpunan penyelesaian persamaan 3 cos 2x+ 5 sin x+1=0, untuk 0≤ x ≤ 2π adalah

Answer 1

Verified answer

TRIGONOMETRI

Interval : 0 ≤ x ≤ 2π

3 cos 2x + 5 sin x + 1 = 0
3(1 - 2 sin² x) + 5 sin x + 1 = 0
-6 sin² x + 5 sin x + 4 = 0
(-2 sin x - 1)(3 sin x - 4) = 0
-2 sin x - 1 = 0
sin x = -1/2 (kuadran 3 dan 4)

sin x = sin (180° + 30°)
x = 210° = 7/6 π

sin x = sin (360° - 30°)
x = 330° = 11/6 π

HP = {7π/6 , 11π/6}