Diketahui persamaan 1+2cos(5x+30°)=0. Himpunan penyelesaian persamaan tersebut untuk 270° ≤ x ≤ 360°) adalah . . .

Jawaban yang benar adalah {306°, 330°} Konsep : Pada kuadran 2 : cos (180° - a) = - cos a Persamaan trigonometri : cos x = cos a ---> x = a + k·360° atau x = - a + k·360° Pembahasan : 1+2cos(5x+30°)=0 2cos(5x+30°) = -1 cos(5x+30°) = -1/2 cos(5x+30°) = -cos 60° cos(5x+30°) = cos (180° - 60°) cos(5x+30°) = cos 120° Maka : 5x + 30° = 120° + k·360° 5x = 120° - 30° + k·360° 5x = 90° + k·360° (dibagi 5) x = 18° + k·72° k = 0 → x = 18° (tidak memenuhi 270° ≤ x ≤ 360°) k = 1 → x = 18° + 72° = 90° (tidak memenuhi 270° ≤ x ≤ 360°) k = 2 → x = 18° + 2·72° = 18° + 144° = 162° (tidak memenuhi 270° ≤ x ≤ 360°) k = 3 → x = 18° + 3·72° = 18° + 216° = 234° (tidak memenuhi 270° ≤ x ≤ 360°) k = 4 → x = 18° + 4·72° = 18° + 288° = 306° k = 5 → x = 18° + 5·72° = 18° + 360° = 398° (tidak memenuhi 270° ≤ x ≤ 360°) Atau : 5x + 30° = -120° + k·360° 5x = -120° - 30° + k·360° 5x = -150° + k·360° (dibagi 5) x = -30° + k·72° k = 0 → x = -30° (tidak memenuhi 270° ≤ x ≤ 360°) k = 1 → x = -30° + 72° = 42° (tidak memenuhi 270° ≤ x ≤ 360°) k = 2 → x = -30° + 2·72° = -30° + 144° = 114° (tidak memenuhi 270° ≤ x ≤ 360°) k = 3 → x = -30° + 3·72° = -30° + 216° = 186° (tidak memenuhi 270° ≤ x ≤ 360°) k = 4 → x = -30° + 4·72° = -30° + 288° = 258°(tidak memenuhi 270° ≤ x ≤ 360°) k = 5 → x = -30° + 5·72° = -30° + 360° = 330° k = 6 → x = -30° + 6·72° = -30° + 432° = 402° (tidak memenuhi 270° ≤ x ≤ 360°) Jadi himpunan penyelesaian persamaan tersebut adalah {306°, 330°}