Question

Tentukan hp dari 3sec^2 2x = 4

Answer 1

Verified answer

3 sec² 2x = 4
3/(cos² 2x) = 4
3 = 4 cos² 2x
cos² 2x = 3/4
cos 2x = ± √(3/4)
cos 2x = ± 1/2 √3

1) cos 2x = 1/2 √3
cos 2x = cos 30°
2x = 30° + k . 360° atau 2x = -30° + k . 360°
x = 15° + k . 180° ............... x = -15° + k . 180°
x = 15° ................................. x = -15° (TM) => untuk k = 0
x = 195° .............................. x = 165° => untuk k = 1
x = 375° (TM) .................... x = 345° => untuk k = 2

2) cos 2x = -1/2 √3
cos 2x = cos 150°
2x = 150° + k . 360° atau 2x = -150° + k . 360°
x = 75° + k . 180° ................. x = -75° + k . 180°
x = 75° ................................... x = -75° (TM) => untuk k = 0
x = 255° ................................ x = 105° => untuk k = 1
x = 435° (TM) ....................... x = 285° => untuk k = 2

Jika interval : 0 ≤ x ≤ 360°
HP = {15°, 75°, 105°, 165°, 195°, 255°, 285°, 375°}

TM = tidak memenuhi