Hp dari sin 3x = sin 60° untuk 0 ≤ x ≤ 360° adalah. Tolong bantu

Matematika Peminatan
Persamaan Trigonometri XI SMA

Pembahasan :
Batas Interval
0 ≤ x ≤ 360°

Sin 3x = Sin 60°

3x = 60° + K . 360°
x = 20° + K . 120°

3x = (180 - 60)° + K . 360°
x = 40° + K . 120°

Misal K = 0, maka :
x = 20°
x = 40°

Misal K = 1, maka :
x = 140°
x = 160°

Misal K = 2, maka :
x = 260°
x = 280°

Misal K = 3, maka :
x = 380° (TM)
x = 400° (TM)

Hp : {20° , 40° , 140° , 160° , 260° , 280°}

Bab : Persamaan Trigonometri
kelas : XI SMA

sin 3x = sin 60
3x = 60
x = 20 

x = α + k . 360
k = 0 => x = 20° + 0 . 360 = 20° ( M )
k = 1 => x = 20° + 1 . 360 = 380° ( TM )

x = (180 - α) + k . 360
x = 180 - 20 + k . 360
x = 160 + k . 360 

k = 0 => x = 160° + 0.360 = 160° (M)
k = 1 => x = 160° + 1 . 360 = 520° ( TM  )

Hp = { 20° , 160° }