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  4. The number of values of x in the interval [0 , 5 π ] satisfying the equation 3sin2 x-7sin ⁡ x+2=0 is

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

NTA AbhyasNTA Abhyas 2020

Solution:

$3sin^{2} x-7sin ⁡ x+2=0$
$3sin^{2} x-6sin ⁡ x-sin ⁡ x+2=0$
$\left(3 sin x - 1\right)\left(sin ⁡ x - 2\right)=0$
$\Rightarrow sin x=\frac{1}{3},sin ⁡ x=2$ not possible
Solution
Fro the figure, $6$ roots in $\left[0 , 5 \pi \right]$