The {\tt psplot} command is powerful. This allows you to create graphs.


{\bf An important note: } if you want your work to work on {\it both} Web and paper, you must specify {\tt algebraic} in the parameters. This platform actually uses JavaScript syntax for evaluating the formulae, which is almost identical to the syntax used normally.


\psset{unit=0.5}
\begin{center}
\begin{pspicture}(-13,-1.25)(13,3)

\psplot[algebraic,linewidth=1.5pt,plotpoints=1000]{-12.56}{12.56}{2*sin(x)/x}
\psaxes[showorigin=false,labels=none, Dx=3.14](0,0)(-12.6,0)(12.6,0)
\rput(5.7, 1){$a/b$}
\psline[linestyle=dashed](0,2)(5,2)
\psline{<->}(5,0)(5,2)
\rput(3.14, -0.5){$\frac{\pi}{a}$}
\rput(6.28, -0.5){$\frac{2\pi}{a}$}
\rput(9.42, -0.5){$\frac{3\pi}{a}$}
\rput(12.56, -0.5){$\frac{4\pi}{a}$}
\rput(-3.14, -0.5){$\frac{-\pi}{a}$}
\rput(-6.28, -0.5){$\frac{-2\pi}{a}$}
\rput(-9.42, -0.5){$\frac{-3\pi}{a}$}
\rput(-12.56, -0.5){$\frac{-4\pi}{a}$}
\rput(0, -0.5){$0$}

% begin x-axis labels:
\psline(-6.2831853, -0.1)(-6.2831853, 0.1)
\psline(-4.712388975, -0.1)(-4.712388975, 0.1)
\psline(-3.14159265, -0.1)(-3.14159265, 0.1)
\psline(-1.570796325, -0.1)(-1.570796325, 0.1)
\psline(0, -0.1)(0, 0.1)
\psline(1.570796325, -0.1)(1.570796325, 0.1)
\psline(3.14159265, -0.1)(3.14159265, 0.1)
\psline(4.712388975, -0.1)(4.712388975, 0.1)
\psline(6.2831853, -0.1)(6.2831853, 0.1)
% end x-axis labels:


\end{pspicture}
\end{center}


\begin{verbatim}
\begin{pspicture}(-13,-1.25)(13,3)
\psplot[algebraic,linewidth=1.5pt,plotpoints=1000]{-12.56}{12.56}{2*sin(x)/x}
\psaxes[showorigin=false,labels=none, Dx=3.14](0,0)(-12.6,0)(12.6,0)
\rput(5.7, 1){$a/b$}
\psline[linestyle=dashed](0,2)(5,2)
\psline{<->}(5,0)(5,2)
\rput(3.14, -0.5){$\frac{\pi}{a}$}
\rput(6.28, -0.5){$\frac{2\pi}{a}$}
\rput(9.42, -0.5){$\frac{3\pi}{a}$}
\rput(12.56, -0.5){$\frac{4\pi}{a}$}
\rput(-3.14, -0.5){$\frac{-\pi}{a}$}
\rput(-6.28, -0.5){$\frac{-2\pi}{a}$}
\rput(-9.42, -0.5){$\frac{-3\pi}{a}$}
\rput(-12.56, -0.5){$\frac{-4\pi}{a}$}
\rput(0, -0.5){$0$}
\psline(-6.2831853, -0.1)(-6.2831853, 0.1)
\psline(-4.712388975, -0.1)(-4.712388975, 0.1)
\psline(-3.14159265, -0.1)(-3.14159265, 0.1)
\psline(-1.570796325, -0.1)(-1.570796325, 0.1)
\psline(0, -0.1)(0, 0.1)
\psline(1.570796325, -0.1)(1.570796325, 0.1)
\psline(3.14159265, -0.1)(3.14159265, 0.1)
\psline(4.712388975, -0.1)(4.712388975, 0.1)
\psline(6.2831853, -0.1)(6.2831853, 0.1)
\end{pspicture}
\end{verbatim}



\begin{center}
\psset{xunit=1,yunit=2}
\begin{pspicture}(-8,-2)(8,2)
    

\psplot[algebraic,linewidth=2pt,fillstyle=solid, fillcolor=lightblue]{-3.14}{3.14}{sin(x)}
\psplot[algebraic,linewidth=2pt]{-6.2831}{6.2831}{sin(x)}

% function name
\rput(6.2831853,1.3){$\left|H(\omega)\right|$}

% x-axis
\psline(-6.6831853, 0)(6.6831853, 0)
\rput(6.6831853,-0.3){$\omega$}

% begin x-axis labels:
\psline(-6.2831853, -0.1)(-6.2831853, 0.1)
\rput(-6.2831853, -0.3){$-2\pi$}
\psline(-4.712388975, -0.1)(-4.712388975, 0.1)
\rput(-4.712388975, -0.3){$-\frac{3\pi}{2}$}
\psline(-3.14159265, -0.1)(-3.14159265, 0.1)
\rput(-3.14159265, -0.3){$-\pi$}
\psline(-1.570796325, -0.1)(-1.570796325, 0.1)
\rput(-1.570796325, -0.3){$-\frac{\pi}{2}$}
\psline(0, -0.1)(0, 0.1)
\rput(0, -0.3){$0$}
\psline(1.570796325, -0.1)(1.570796325, 0.1)
\rput(1.570796325, -0.3){$\frac{\pi}{2}$}
\psline(3.14159265, -0.1)(3.14159265, 0.1)
\rput(3.14159265, -0.3){$\pi$}
\psline(4.712388975, -0.1)(4.712388975, 0.1)
\rput(4.712388975, -0.3){$\frac{3\pi}{2}$}
\psline(6.2831853, -0.1)(6.2831853, 0.1)
\rput(6.2831853, -0.3){$2\pi$}
% end x-axis labels:
\end{pspicture}
\end{center}

\begin{verbatim}
\begin{pspicture}(-8,-2)(8,2)
\psplot[algebraic,linewidth=2pt,fillstyle=solid, fillcolor=lightblue]{-3.14}{3.14}{sin(x)}
\psplot[algebraic,linewidth=2pt]{-6.2831}{6.2831}{sin(x)}
\rput(6.2831853,1.3){$\left|H(\omega)\right|$}
\psline(-6.6831853, 0)(6.6831853, 0)
\rput(6.6831853,-0.3){$\omega$}
\psline(-6.2831853, -0.1)(-6.2831853, 0.1)
\rput(-6.2831853, -0.3){$-2\pi$}
\psline(-4.712388975, -0.1)(-4.712388975, 0.1)
\rput(-4.712388975, -0.3){$-\frac{3\pi}{2}$}
\psline(-3.14159265, -0.1)(-3.14159265, 0.1)
\rput(-3.14159265, -0.3){$-\pi$}
\psline(-1.570796325, -0.1)(-1.570796325, 0.1)
\rput(-1.570796325, -0.3){$-\frac{\pi}{2}$}
\psline(0, -0.1)(0, 0.1)
\rput(0, -0.3){$0$}
\psline(1.570796325, -0.1)(1.570796325, 0.1)
\rput(1.570796325, -0.3){$\frac{\pi}{2}$}
\psline(3.14159265, -0.1)(3.14159265, 0.1)
\rput(3.14159265, -0.3){$\pi$}
\psline(4.712388975, -0.1)(4.712388975, 0.1)
\rput(4.712388975, -0.3){$\frac{3\pi}{2}$}
\psline(6.2831853, -0.1)(6.2831853, 0.1)
\rput(6.2831853, -0.3){$2\pi$}
\end{pspicture}
\end{verbatim}

\psset{unit=1cm}
\begin{center}
\begin{pspicture}(-3.5,-3.25)(3.5,2)
\psplot[algebraic,linewidth=1.5pt]{-3.14}{3.14}{cos(x/2)}
\psaxes[showorigin=false,labels=none, Dx=3.14](0,0)(-3.25,0)(3.25,0)
\rput(3.14, -0.35){$\pi$}
\rput(-3.14, -0.35){$-\pi$}
\rput(0, -0.35){$0$}
\rput(1.25,1.25 ){$\left| H(\omega) \right| =\cos(\omega/2)$}
\end{pspicture}
\end{center}

\begin{verbatim}
\begin{pspicture}(-3.5,-3.25)(3.5,2)
\psplot[algebraic,linewidth=1.5pt]{-3.14}{3.14}{cos(x/2)}
\psaxes[showorigin=false,labels=none, Dx=3.14](0,0)(-3.25,0)(3.25,0)
\rput(3.14, -0.35){$\pi$}
\rput(-3.14, -0.35){$-\pi$}
\rput(0, -0.35){$0$}
\rput(1.25,1.25 ){$\left| H(\omega) \right| =\cos(\omega/2)$}
\end{pspicture}
\end{verbatim}

\begin{center}
\begin{pspicture}(-3.5,-1.25)(3.5,2)
\psplot[algebraic,linewidth=1.5pt]{-3.14}{3.14}{abs(sin(x/2))}
\psaxes[showorigin=false,labels=none, Dx=3.14](0,0)(-3.25,0)(3.25,0)
\rput(3.14, -0.35){$\pi$}
\rput(-3.14, -0.35){$-\pi$}
\rput(0, -0.35){$0$}
\rput(1,1.25 ){$\left| G(\omega) \right| =\left| \sin(\omega/2) \right|$}
\end{pspicture}
\end{center}

\begin{verbatim}
\begin{pspicture}(-3.5,-1.25)(3.5,2)
\psplot[algebraic,linewidth=1.5pt]{-3.14}{3.14}{abs(sin(x/2))}
\psaxes[showorigin=false,labels=none, Dx=3.14](0,0)(-3.25,0)(3.25,0)
\rput(3.14, -0.35){$\pi$}
\rput(-3.14, -0.35){$-\pi$}
\rput(0, -0.35){$0$}
\rput(1,1.25 ){$\left| G(\omega) \right| =\left| \sin(\omega/2) \right|$}
\end{pspicture}
\end{verbatim}