Himpunan penyelesaian dari persamaan cos 2x = cos x

Bab Trigonometri
Matematika SMA Kelas X

cos 2x = cos x
cos 2x - cos x = 0
2 cos² x - 1 - cos x = 0
2 cos² x - cos x - 1 = 0
(2 cos x + 1) (cos x - 1) = 0
2 cos x + 1 = 0
2 cos x = -1
cos x = -1/2
x = 120°, 240°

cos x - 1 = 0
cos x = 1
x = 0°, 360°

HP = { 0°, 120°, 240°, 360° }

TriGonoMetRi

cos 2x = cos x
cos 2x - cos x = 0
2 cos² x - 1 - cos x = 0
(2 cos x + 1)(cos x - 1) = 0

Pembuat nol :
2 cos x + 1 = 0
cos x = -1/2
cos x = cos 120° atau cos x = cos 240°
x = ± 120° + k.360°
x = ± 240° + k.360°

cos x - 1 = 0
cos x = 1
x = 0° + k.360°
x = k.360°

Krn interval gk ditentuin, maka :
HP = {± 120° + k.360° , ± 240° + k.360° , k.360° , k bilangan bulat}