Question

Himpunan penyelesaian dari persamaan 2 cos 4x - 1 = 0, untuk 0° ≤ x ≤ 360°

Tolong dibantu lg ya,
Terima kasih

Answer 1

2 cos 4x - 1 = 0
2 cos 4x = 1
cos 4x = 1/2

cos yang hasilnya 1/2 (positif) ---> 60° (Kuadran I) dan 300° (Kuadran IV)

(i) cos 4x = cos 60 + k.360
4x = 60 + k.360
x = 15 + k.90

k = 0 ---> x = 15 + 0.90 = 15 + 0 = 15°
k = 1 ---> x = 15 + 1.90 = 15 + 90 = 105°
k = 2 ---> x = 15 + 2.90 = 15 + 180 = 195°
k = 3 ---> x = 15 + 3.90 = 15 + 270 = 285°

(ii) cos 4x = cos 300 + k.360
4x = 300 + k.360
x = 75 + k.90

k = 0 ---> x = 75 + 0.90 = 75 + 0 = 75°
k = 1 ---> x = 75 + 1.90 = 75 + 90 = 165°
k = 2 ---> x = 75 + 2.90 = 75 + 180 = 255°
k = 3 ---> x = 75 + 3.90 = 75 + 270 = 345°

HP = {15°, 75°, 105°, 165°, 195°, 255°, 285°, 345°}