Answer: -3
First, let us find the value of A(x).
We know that A(x) = f(x) - g(x)
Given that:


We know that

Using trigonometric identities, we can rewrite this as

Subtract, and we will get

Now, to find it's minimum value, we will plug in 3π/2 from the interval to 2sin(θ)-1, and we will get a value of y = -3.
Therefore, the minimum value of A(x) is -3.