How many values of \(x\) satisfy the equation \[2 \cos^2x + 5\sin x = 4\] in the range \(0 \leq x < 2 \pi\)?

\(2\),

\(4\),

\(6\),

\(8\).

so \(\sin x = \frac{1}{2}\) (since \(\sin x = 2\) is impossible).

This occurs at \(x = \dfrac{\pi}{6}\) and \(x = \dfrac{5\pi}{6}\) in the given range, so there are \(2\) such values of \(x\) and the answer is (a).