sin (5x – 24°) = sin 46°, 0° ≤ x ≤ 360°
Tentukan himpunan penyelesaian dari persamaan persamaan trigonometri berikut!
sin (5x – 24°) = sin 46°, 0° ≤ x ≤ 360°
Jawab:
sin (5x – 24°) = sin 46°, sehingga diperoleh
a. 5x – 24° = 46° + k . 360°
5x = 70° + k . 360°
x = 14° + k . 72°
k = 0 → x = 14° + 0 . 72° = 14°
k = 1 → x = 14° + 1 . 72° = 86°
k = 2 → x = 14° + 2 . 72° = 158°
k = 3 → x = 14° + 3 . 72° = 230°
k = 4 → x = 14° + 4 . 72° = 302°
k = 5 → x = 14° + 5 . 72° = 374° (Tidak memenuhi)
b. 5x – 24° = (180° – 46°) + k . 360°
5x = 134° + 24° + k . 360°
5x = 158° + k . 360°
x = 31,6° + k . 72°
k = 0 → x = 31,6° + 0 . 72° = 31,6°
k = 1 → x = 31,6° + 1 . 72° = 103,6°
k = 2 → x = 31,6° + 2 . 72° = 175,6°
k = 3 → x = 31,6° + 3 . 72° = 247,6°
k = 4 → x = 31,6° + 4 . 72° = 319,6°
k = 5 → x = 31,6° + 5 . 72° = 391,6° (Tidak memenuhi)
Jadi himpunan penyelesaiannya adalah {14°, 31,6°, 86°, 103,6°, 158°, 175,6°, 230°, 247,6°, 302°, 319,6°}
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