Question

Himpunan penyelesaian persamaan sin² 2x - 2 sin x cos x = 0, untuk 0° ≤ x ≤ 360° adalah....


pakai cara y,
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Answer 1

Verified answer

Kelas 11 Matematika
Bab Trigonometri Lanjut

sin² 2x - 2 sin x cos x = 0
sin² 2x - sin 2x = 0
sin 2x (sin 2x - 1) = 0
sin 2x = 0
2x = 0
x = 0°

2x = 180°
x = 180°/2
x = 90°

2x = 360°
x = 360°/2
x = 180°

Kelipatan 90° = { 90°, 180°, 270°, 360°)

sin 2x - 1 = 0
sin 2x = 1
2x = 90°
x = 90°/2
x = 45°

2x = (90° + 360°)
x = 450°/2
x = 225°

HP = { 0°, 45°, 90°, 180°, 225°, 270°, 360°, 0° <= x <= 360° }