\documentclass[12pt]{article}
\setlength{\unitlength}{1mm}
\usepackage[pdftex]{color}
\usepackage[paperwidth=220\unitlength,paperheight=175\unitlength]{geometry}
\setlength{\topmargin}{-36mm}
\setlength{\textwidth}{220\unitlength}
\setlength{\textheight}{175\unitlength}
\setlength{\oddsidemargin}{-23mm}
\setlength{\parindent}{0cm}
\pagestyle{empty}

\definecolor{cS}        {rgb}{0.00,0.00,0.50}   % source coordinates
\definecolor{aS}        {rgb}{0.00,0.00,0.99}   % source auxiliary
\definecolor{cT}        {rgb}{0.50,0.00,0.00}   % target coordinates
\definecolor{aT}        {rgb}{0.99,0.00,0.00}   % target auxiliary
\definecolor{lT}        {rgb}{0.99,0.60,0.60}   % target lengths

\begin{document}
\begin{picture}(215,170)(-65,-10)
% source coordinate system
\thicklines%
\textcolor{cS}{\put(0,-10){\vector(0,1){170}}}%
\textcolor{cS}{\put(-10,0){\vector(1,0){160}}}%
\thinlines%
\textcolor{cS}{\put(90,-2){\line(0,1){4}}}%
\textcolor{cS}{\put(-2,140){\line(1,0){4}}}%
\textcolor{aS}{\put(90,2){\line(0,1){138}}}%
\textcolor{aS}{\put(2,140){\line(1,0){88}}}%
\textcolor{cS}{\put(90,-3){\makebox(0,0)[t]{$x$}}}%
\textcolor{cS}{\put(-3,140){\makebox(0,0)[r]{$y$}}}%
% target coordinate system
\thicklines%
\textcolor{cT}{\put(-8,-4){\vector(2,1){150}}}%
\textcolor{cT}{\put(4,-8){\vector(-1,2){70}}}%
\thinlines%
\textcolor{cT}{\put(-40,75){\line(2,1){4}}}%
\textcolor{aT}{\put(-36,77){\line(2,1){126}}}%
\textcolor{cT}{\put(129,62){\line(-1,2){2}}}%
\textcolor{aT}{\put(127,66){\line(-1,2){40}}}%
\textcolor{cT}{\put(129,62){\makebox(0,0)[t]{$x'$}}}%
\textcolor{cT}{\put(-40,75){\makebox(0,0)[r]{$y'$}}}%
% sin, cos partitioning for x'
\textcolor{aT}{\put(90,0){\line(-1,2){59}}}%
%
\textcolor{lT}{\put(30,20){\vector(-2,-1){32}}}%
\textcolor{lT}{\put(38,24){\vector(2,1){32}}}%
\textcolor{lT}{\put(41,21){\makebox(0,0)[br]{$x \cdot \cos\alpha$}}}%
%
\textcolor{lT}{\put(61,130.500){\vector(2,1){27}}}%
\textcolor{lT}{\put(53,126.500){\vector(-2,-1){21}}}%
\textcolor{lT}{\put(65,127){\makebox(0,0)[br]{$y \cdot \sin\alpha$}}}%
% sin, cos partitioning for y'
\textcolor{aT}{\put(0,140){\line(-2,-1){56}}}%
\textcolor{aT}{\put(0,140){\line(1,-2){18}}}%
\textcolor{lT}{\put(-23,56){\vector(1,-2){27}}}%
\textcolor{lT}{\put(-25,60){\vector(-1,2){27}}}%
\textcolor{lT}{\put(-27,56){\makebox(0,0)[bl]{$y \cdot \cos\alpha$}}}%
%
\textcolor{lT}{\put(4,122){\vector(-1,2){8}}}%
\textcolor{lT}{\put(6,118){\vector(1,-2){8}}}%
\textcolor{lT}{\put(9,122){\makebox(0,0)[tr]{$x \cdot \sin\alpha$}}}%
% point to be rotated
\textcolor{black}{\put(90,140){\circle*{1}}}%
\textcolor{black}{\put(91,141){\makebox(0,0)[bl]{$P$}}}%
% rotation angles
\textcolor{black}{\put(8,2){\makebox(0,0){$\alpha$}}}%
\textcolor{black}{\put(88,10){\makebox(0,0){$\alpha$}}}%
\textcolor{black}{\put(-2,10){\makebox(0,0){$\alpha$}}}%
\textcolor{black}{\put(82,138){\makebox(0,0){$\alpha$}}}%
\end{picture}
\end{document}