Suppose you're given the following Fourier coefficients for a function on the interval $[-\pi,\pi]$: $\displaystyle a_0 = \frac{-2}{2\pi}$, $\displaystyle a_1 = \frac{-2}{\pi}$, $\displaystyle a_2 = \frac{3}{2 \pi}$, $\displaystyle a_3 = \frac{2}{3 \pi}$, $\displaystyle b_1 = \frac{2}{\pi}$, $\displaystyle b_2 = \frac{-2}{2 \pi}$, $\displaystyle b_3 = \frac{-1}{3 \pi}$. Find the following Fourier approximations to the Fourier series $\displaystyle a_0 + \sum_{n=1}^{\infty} (a_n\cos(nx) + b_n\sin(nx))$.

$F_0(x) =$

$F_1(x) =$

$F_2(x) =$

$F_3(x) =$