1 - sin ( 2x + 1/4 phi ) = 0,5

Mapel : Matematika
Kelas : X SMA
Materi : Persamaan Trigono

Pembahasan :
Batas Interval
x ≥ 0 atau x ≤ 2π
0 ≤ x ≤ 2π

1 - Sin (2x + 1/4π) = 0,5
Sin (2x + 1/4π) = 1 - 0,5
Sin (2x + 1/4π) = 0,5
Sin (2x + 1/4π) = Sin 30°
Sin (2x + 1/4π) = Sin 1/6π

2x + 1/4π = 1/6π + K . 2π
2x = 1/6π - 1/4π + K . 2π
2x = (2 - 3)/12π + K . 2π
2x = -1/12π + K . 2π
x = - 1/24π + K . π

2x + 1/4π = 5/6π + K . 2π
2x = 5/6π - 1/4π + K . 2π
2x = (10 - 3)/12π + K . 2π
2x = 7/12π + K . 2π
x = 7/24π + K . π

Misal K = 0, maka :
x = -1/24π (Tidak memenuhi)
x = 7/24π

Misal K = 1, maka :
x = 23/24π
x = 31/24π

Misal K = 2, maka :
x = 47/24π
x = 55/24π (Tidak memenuhi)

Misal K = 3, maka :
x = 71/24π (Tidak memenuhi)
x = 79/24π (Tidak memenuhi)

Maka...
Hp : {7/24π , 23/24π , 31/24π , 47/24π}