Question

The number of values of $x$ in the interval $[0,3\pi ]$ satisfying the equation $2{\text{sin}}^{2}x+5\text{sin}x-3=0$ is

• A. 4
• B. 6
• C. 1
• D. 2

Answer 1

The correct option is A 4

$2{\text{sin}}^{2}x+5\text{sin}x-3=0$
$2{\text{sin}}^{2}x+6\text{sin}x-\text{sin}x-3=0$
$2\text{sin}x(\text{sin}x+3)-1(\text{sin}x+3)=0$
$\text{sin}x=1/2$
Hence $x$ is 4.