What is the number of values of x in the inte | vedclass

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(C) Given the equation: $3\sin^2x - 7\sin x + 2 = 0$Factor the quadratic equation: $(3\sin x - 1)(\sin x - 2) = 0$This gives two possibilities: $\sin

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$6$

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(C) Given the equation: $3\sin^2x - 7\sin x + 2 = 0$Factor the quadratic equation: $(3\sin x - 1)(\sin x - 2) = 0$This gives two possibilities: $\sin x = \frac{1}{3}$ or $\sin x = 2$Since the range of $\sin x$ is $[-1, 1]$,$\sin x = 2$ is impossible.Therefore,we solve for $\sin x = \frac{1}{3}$.In the interval $[0, 2\pi]$,there are $2$ solutions for $\sin x = \frac{1}{3}$.In the interval $[0, 4\pi]$,there are $4$ solutions.In the interval $[0, 5\pi]$,there are $4 + 2 = 6$ solutions,as the interval $[4\pi, 5\pi]$ contains $2$ additional solutions.

What is the number of values of $x$ in the interval $[0, 5\pi]$ that satisfy the equation $3\sin^2x - 7\sin x + 2 = 0$?

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