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

Answer: (A)

$2si{n}^{2}x+5sinx-3=0$
$\Rightarrow sinx=\frac{1}{2}$, as $sinx\ne -3$
For $0^{\circ }\le x\le 540^{\circ }$, the values of $x$ are $30^{\circ }$, $150^{\circ },390^{\circ },510^{\circ }$.
$\therefore$ Number of values are $4$.