Jawab:

{-8π/9, -4π/9, -2π/9, 2π/9, 4π/9, 8π/9}

Penjelasan dengan langkah-langkah:

cos 3x = -1/2, -π ≤ x ≤ π

Saya konversi ke derajat dulu untuk mempermudah perhitungan

cos 3x = -1/2, -180° ≤ x ≤ 180°

cos 3x = cos 120°

cos u = cos α

u = ± α + k(360°), k bilangan bulat

3x = ± 120° + k(360°)

x = ± 40° + k(120°)



k = -1 → x = 40° - 1(120°) = -80°

k = 0 → x = 40° + 0(120°) = 40°

k = 1 → x = 40° + 1(120°) = 160°

k = -1 → x = -40° - 1(120°) = -160°

k = 0 → x = -40° + 0(120°) = -40°

k = 1 → x = -40° + 1(120°) = 80°

HP = {-160°, -80°, -40°, 40°, 80°, 160°}

= {-8π/9, -4π/9, -2π/9, 2π/9, 4π/9, 8π/9}

Catatan

Konversi radian ke derajat

... rad = ... × 180°/π

Konversi derajat ke radian

...° = ... × π/180 rad