#### Answer

$(-2, 2, 3)$

#### Work Step by Step

The $x$ component, $-2+cos(t)$, oscillates between $-3$ and $-1$, so its center in the x-dimension is $-2$.
The $y$ component is the constant $2$, so its center in the y-dimension is $2$.
The $z$ component, $3-sin(t)$, oscillates between $2$ and $4$, so its center in the z-dimension is $3$.
Therefore, the coordinates of the center are $(-2, 2, 3)$.