Which of the following is the solution to the differential equation \(\dfrac{dy}{dx}=3\sin x\) with the initial condition \(y(\pi)=-1\) ?

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Take the antiderivative of \(\dfrac{dy}{dx} \):

$$ \int \frac{dy}{dx}=\int 3\sin x $$ $$ y = -3\cos x + C $$

Using the initial condition:

$$ -1 = -3\cos (\pi)+C $$ $$ -1=3+C $$ $$ C=-4 $$ $$ \boxed{y=-3\cos x-4} $$