Question

$\text{The number of values of x in the interval}[0,5\pi ]satisfyingtheequation3si{n}^{2}x-7sinx+2=0is$

• A. 0
• B. 5
• C. 6
• D. 10

Answer 1

The correct option is C

6

$Given:3si{n}^{2}x-7sinx+2=0\Rightarrow 3si{n}^{2}x-6sinx-sinx+2=0\Rightarrow 3sinx(sinx-2)-1(sinx-2)=0\Rightarrow (3sinx-1)=0orsinx-2=0\text{Now,sin x=2 is not possible,as the value of sin x lies between-1 and 1.}\Rightarrow sinx=\frac{1}{3}\text{Also, sin x is positive only in first two quadrants. Therefore sin x is positive twice in the interval}[0,\pi ]\text{Hence,it is positive six times in the interval}[0,5\pi ],v/z[0,\pi ],[2\pi ,3\pi ]and[4\pi ,5\pi ].$