solve cos(2x)-3sin(x)-2=0

Question

please someone help. what do i do?

Answer 1

cos(2x)=1-2sin²(x).

1-2sin²(x)-3sin(x)-2=0,

2sin²(x)+3sin(x)+1=0=(2sin(x)+1)(sin(x)+1),

sin(x)=-½ or -1; x=-π/6+2πn, -5π/6+2πn, -π/2+2πn, where n is an integer. To convert x into degrees use π=180°. So x=11π/6 (330°), 7π/6 (210°), 3π/2 (270°), 7π/2 (630°), etc.