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

Answer: (C)

6

Given, $3{\sin }^{2}x-7\sin x+2=0$

$(3\sin x-1)(\sin x-2)=0$

but $-1\le \sin x\le 1$

so only solution is,
$\sin x=\frac{1}{3}=\sin \alpha$, where $\alpha ={\sin }^{-1}\left(\frac{1}{3}\right)$

Hence general solution is,
$x=n\pi +(-1{)}^n\alpha$

In $[0,5\pi ]$ solution is $x=\alpha ,\pi -\alpha ,2\pi +\alpha ,3\pi -\alpha ,4\pi +\alpha ,5\pi -\alpha$