\documentclass[12pt, a4paper]{article}
\pagestyle{empty}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{times}
\usepackage[italian]{babel}

\newcommand{\cotg}{\mbox{cotg}}
\newcommand{\sen}{\mbox{sen}}
\newcommand{\tg}{\mbox{tg}}
\newcommand{\za}{\alpha}
\newcommand{\zb}{\beta}
\newcommand{\zg}{\gamma}

\begin{document}

\centerline{\bf Funzioni Trigonometriche}
\bigskip

Formule importanti:
$$\sen^2(\za)+\cos^2(\za)=1,\qquad\tg(\za)=\frac{\sen(\za)}{\cos(\za)}.$$
$$\begin{cases}
\sen(\za+\zb)=\sen(\za)\cos(\za)+\cos(\za)\sen(\za);\\
\sen(\za-\zb)=\sen(\za)\cos(\za)-\cos(\za)\sen(\za);\\
\cos(\za+\zb)=\cos(\za)\cos(\zb)-\sen(\za)\sen(\zb);\\
\cos(\za-\zb)=\cos(\za)\cos(\zb)+\sen(\za)\sen(\zb).
\end{cases}$$
$$\begin{cases}
\sen(2\za)=2\sen(\za)\cos(\za);\\
\cos(2\za)=\cos^2(\za)-\sen^2(\za)=2\cos^2(\za)-1=1-2\sen^2(\za).
\end{cases}$$
\bigskip

Semplificare le seguenti espressioni:
\begin{itemize}
\item[1-4.] $\cos(\pi-\za)$, $\tg(\pi+\za)$, $\sen(2\pi-\za)$, $\cos(-\za)$;
\item[5-8.] $\tg(\pi-\za)$, $\cos(3\pi-\za)$, $\sen(\pi+\za)$, $\sen(\pi-\za)$;
\item[9-12.] $\sen(\frac{\pi}{2}-\za)$, $\cos(\frac{\pi}{2}+\za)$,
$\tg(\frac{3\pi}{2}-\za)$, $\sen(\frac{3\pi}{2}+\za)$;
\item[13-16.] $\sen(\frac{\pi}{2}+\za)$, $\cos(\frac{\pi}{2}-\za)$,
$\tg(\frac{3\pi}{2}+\za)$, $\sen(\frac{3\pi}{2}-\za)$;
\item[17-20.] $1-\sen^2(\za)$, $1+\tg^2(\za)$, $\frac{1}{\tg(\za)}$,
$\cos^2(\za)-1$.
\end{itemize}
\medskip

Risolvere le seguenti equazioni:
\begin{itemize}
\item[21.] $\sen(x)=-\frac{1}{2}\sqrt{2}$, $\cos(x)=\frac{1}{2}\sqrt{3}$,
$\tg(x)=-1$, $\sen(x)=\frac{1}{2}$;
\item[22.] $\cos(x)=-\frac{1}{2}$, $\cos(x)=\frac{1}{2}\sqrt{2}$,
$\tg(x)=-\sqrt{3}$, $\cos(x)=-\frac{1}{2}\sqrt{3}$;
\item[23.] $\tg(x)=0$, $\sen(x)=-1$, $\cos(x)=0$, $\cos(x)=-1$;
\item[24.] $\tg(x)=\frac{1}{3}\sqrt{3}$, $\cotg(x)=1$, $\sen(x)=-\frac{1}{2}$,
$\cos(x)=-\frac{1}{2}\sqrt{3}$.
\end{itemize}
\medskip

Tracciare i grafici delle seguenti funzioni:
\begin{itemize}
\item[25-28.] $\sen(x)$, $\cos(x)$, $\tg(x)$, $\cotg(x)$;
\item[29-32.] $\sen(2x)$, $\cos(3x)$, $\tg(x/2)$, $\tg(\pi-x)$;
\item[33-36.] $\sen(x+\frac{\pi}{4})$, $\cos(\frac{\pi}{3}-x)$, $\cos(x+\pi)$,
$\tg(\frac{\pi}{4}-x)$;
\item[37-40.] $\tg(-2x)$, $\sen(\pi-2x)$, $\cos(\pi+3x)$, $\cos(2x-\pi)$.
\end{itemize}

\end{document}
