Question

2sin(2x-π/4)=√3 untuk 0<x<2π. tentukan himpunan penyelesaiannya dan cara kerjanya.
tolong dong! besok pagi dikumpulkan jam 7 pagi.

Answer 1

Verified answer

Bab Trigonometri
Matematika SMA Kelas X

2 sin (2x - π/4) = √3
sin (2x - π/4) = 1/2 . √3
2x - π/4 = π/3
2x = π/4 + π/3
2x = 3π/12 + 4π/12
x = 7π/12 . 1/2
x = 7π/24

2x - π/4 = 2π/3
2x = π/4 + 2π/3
2x = 3π/12 + 8π/12
x = 11π/12 . 1/2
x = 11π/24

2x - π/4 = π/3 + 1 . 2π
2x = (π/4 + π/3) + 24π/12
2x = 7π/12 + 24π/12
x = 31π/12 . 1/2
x = 31π/24

2x - π/4 = 2π/3 + 1 . 2π
2x = (π/4 + 2π/3) + 24π/12
2x = 11π/12 + 24π/12
x = 35π/12 . 1/2
x = 35π/24

HP = { 7π/24, 11π/24, 31π/24; 35π/24, 0 < x < 2π }