Question

The number of values of $x$ in the interval $[0,5\pi ]$ satisfying the equation $3{\sin }^{2}x-7\sin x+2=0$ is

• A. $0$
• B. $5$
• C. $6$
• D. $10$

Answer 1

The correct option is C $6$

Given quadratic equation
$3{\sin }^{2}x-7\sin x+2=0$
$\Rightarrow (3\sin x-1)(\sin x-2)=0$
$\sin x=\frac{1}{3},2$
But, $\sin x\ne 2$
So, $\sin x=\frac{1}{3}$
In the interval [0, 5$\pi$] there are $6$ solutions .