solve the equation 2sin2x+3sinx+1=0

Question

Solve the equation and write the answers as a general solution to

2sin2x+3sinx+1=0

Answer 1

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

Therefore sin(x)=-½ or -1.

So x=-π/6, -5π/6 or -π/2. To make these more general we need to add 2nπ where n is any integer.

When n=1: x=11π/6, 7π/6, or 3π/2. When n=2: x=23π/6, 19π/6, 7π/2, etc.

To convert to degrees, substitute π=180°, which makes π/6=30°.