(D) Let $f(\theta) = 5 \sin^2 \theta + 4 \cos^2 \theta$. Using the identity $\sin^2 \theta + \cos^2 \theta = 1$,we can write $\cos^2 \theta = 1 - \sin

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(D) Let $f(\theta) = 5 \sin^2 \theta + 4 \cos^2 \theta$. Using the identity $\sin^2 \theta + \cos^2 \theta = 1$,we can write $\cos^2 \theta = 1 - \sin^2 \theta$. Substituting this into the expression: $f(\theta) = 5 \sin^2 \theta + 4(1 - \sin^2 \theta)$ $f(\theta) = 5 \sin^2 \theta + 4 - 4 \sin^2 \theta$ $f(\theta) = 4 + \sin^2 \theta$. Since the minimum value of $\sin^2 \theta$ is $0$,the minimum value of $f(\theta)$ is $4 + 0 = 4$.