Persamaan Trigonometri
√3 sin x = 1 - cos x
Kuadratkan kedua ruas
3 sin² x = 1 - 2 cos x + cos² x
3 (1 - cos² x) - 1 + 2 cos x - cos² x = 0
-4 cos² x + 2 cos x + 2 = 0
2 cos² x - cos x - 1 = 0
(2 cos x + 1)(cos x - 1) = 0
0° ≤ x ≤ 360°
2 cos x + 1 = 0
cos x = -1/2 → x = 120°, 240°
cos x - 1 = 0
cos x = 1 → x = 0° , 360°
Nilai x yg memenuhi :
0°, 120°, 240°, 360°
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Persamaan Trigonometri
√3 sin x = 1 - cos x
Kuadratkan kedua ruas
3 sin² x = 1 - 2 cos x + cos² x
3 (1 - cos² x) - 1 + 2 cos x - cos² x = 0
-4 cos² x + 2 cos x + 2 = 0
2 cos² x - cos x - 1 = 0
(2 cos x + 1)(cos x - 1) = 0
0° ≤ x ≤ 360°
2 cos x + 1 = 0
cos x = -1/2 → x = 120°, 240°
cos x - 1 = 0
cos x = 1 → x = 0° , 360°
Nilai x yg memenuhi :
0°, 120°, 240°, 360°