tan 5x = - 1/3√3, 0° ≤ x ≤ 360°
Tentukan himpunan penyelesaian dari persamaan trigonometri berikut!
tan 5x = - 1/3√3, 0° ≤ x ≤ 360°
Pembahasan:
tan 5x = - 1/3√3 = tan 150°, sehingga diperoleh:
5x = 150° + k . 180°
x = 30° + k . 36°
k = 0 → x = 30°
k = 1 → x = 30° + 36° = 66°
k = 2 → x = 30° + 72° = 102°
k = 3 → x = 30° + 108° = 138°
k = 4 → x = 30° + 144° = 174°
k = 5 → x = 30° + 180° = 210°
k = 6 → x = 30° + 216° = 246°
k = 7 → x = 30° + 252° = 282°
k = 8 → x = 30° + 288° = 318°
k = 9 → x = 30° + 324° = 354°
Jadi, himpunan penyelesaiannya adalah {66°, 102°, 138°, 174°, 210°, 246°, 282°, 318°, 354°}
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