Construct the first three Fourier approximations to the square wave function $$f(x) = \begin{cases}-1 & -\pi \le x < 0\cr 1 & 0 \le x < \pi\end{cases}$$

$F_1(x) =$
$F_2(x) =$
$F_3(x) =$

Using a calculator, graph the function and the first three Fourier approximations to see how the approximation matches the function $f(x)$.