Question

Berapakah Himpunan Penyelesaian dari: (Sin 3x - cos 4x)(cos 5x - sin 4x) = 0
(cot (2x+60°)+√3)(sec 3x - √2) = 0
2 sin² x + 5 cos x + 1 = 0
dengan 0° ≤ x ≤ 360° ?

Answer 1

Verified answer

1) sin 3x - cos 4x = 0
sin 3x = cos 4x
sin 3x = sin (90-4x)
3x = 90 - 4x
3x + 4x = 90
7x = 90
x = (90/7)°
cos 5x - sin 4x = 0
cos 5x = sin 4x
cos 5x = cos (90-4x)
5x = 90 - 4x
5x + 4x = 90
9x = 90
x = 10°
2) cot (2x+60) + √3 = 0
cot (2x + 60) = -√3
cot (2x + 60) = cot 120
2x + 60 = 120
2x = 60
x = 30
cot (2x + 60) = cot 300
2x + 60 = 300
2x = 240
x = 120
cot (2x + 60) = cot 480
2x + 60 = 480
2x = 420
x = 210
cot (2x + 60) = cot 660
2x + 60 = 660
2x = 600
x = 300
sec 3x - √2 = 0
sec 3x = √2
sec 3x = sec 45
3x = 45
x = 15
sec 3x = sec 315
3x = 315
x = 105
sec 3x = 405
3x = 405
x = 135
sec 3x = sec 675
3x = 675
x = 215
sec 3x = sec 765
3x = 765
x = 255
sec 3x = 1035
3x = 1035
x = 345
hp{15°, 30°, 105°, 120°, 135°, 210°, 215°, 255°, 300°, 345°}
3) 2sin²x + 5 cos x + 1 = 0
2(1 - cos²x) + 5 cos x + 1 = 0
2 - 2cos²x + 5cos x + 1 = 0
-2.cos²x + 5.cos x + 3 = 0
2.cos²x - 5.cos x - 3 = 0
(2.cos x + 1)(cos x - 3) = 0
cos x - 3 = 0
cos x = 3 (tidak memenuhi)
2.cos x + 1 = 0
2.cos x = -1
cos x = -½
cos x = cos 120
x = 120
cos x = cos 240
x = 240
hp {120°,240°}