8.045. $2 \cos ^{2} x+5 \sin x-4=0$.

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8.045. $2 \cos ^{2} x+5 \sin x-4=0$.
## Solution.

We have $2\left(1-\sin ^{2} x\right)+5 \sin x-4=0$ or $2 \sin ^{2} x-5 \sin x+2=0$. Solving this equation as a quadratic equation in terms of $\sin x$, we get $\sin x=2, \varnothing$, or $\sin x=\frac{1}{2}, x=(-1)^{k} \frac{\pi}{6}+\pi k, \quad k \in Z$.

Answer: $\quad x=(-1)^{k} \frac{\pi}{6}+\pi k, \quad k \in Z$.