Question

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

• A. 4
• B. 6
• C. 1
• D. 2

Answer 1

The correct option is B 6

$2si{n}^{2}x+5sinx-3=0\Rightarrow (sinx+3)(2sinx-1)=0\Rightarrow sinx=\frac{1}{2}\Rightarrow x=\frac{\pi }{6},\frac{5\pi }{6},\frac{7\pi }{6},\frac{11\pi }{6},\frac{13\pi }{6},\frac{17\pi }{6}$