Question

Tolong dibantu ya
himpunan penyelesaian persamaan cos 2x + 7 sin x - 4 = 0 adalah ..
a.240°,300°
b.210°,330°
c.120°,240°
d.30°,150°
e.60°,120°

Answer 1

Cos 2x + 7 sin x -4 = 0
(1 - 2 sin² x) + 7 sin x - 4 = 0
-2 sin²x + 7 sin x - 3 = 0
(-2 sin x + 1)(sin x - 3) = 0
-2 sin x + 1 = 0 atau sin x - 3 = 0

ambil
-2 sin x + 1 = 0
-2 sin x = -1
sin x = 1/2
sin x = sin 30
x = 30 + k.360
k = 0 ==> x = 150

atau
x = (180 - 30) + k.360
k = 0 , x = 150