File:AcosplotT.png

Explicit plot of function ArcCos.

\(y=\mathrm{acos}(x)\)

is plotted versus \(x\).

C++ generator of curve

//File ado.cin should be loaded in the cuffent directory for the compilation of the C++ code below:

 #include <math.h> 
 #include <stdio.h>
 #include <stdlib.h>
 #define DB double 
 #define DO(x,y) for(x=0;x<y;x++)
 using namespace std;
 #include <complex>
 typedef complex<double> z_type;
 #define Re(x) x.real()
 #define Im(x) x.imag()
 #define I z_type(0.,1.)
 #include "ado.cin"

 z_type acos(z_type z){
 if(Im(z)<0){if(Re(z)>=0){return  I*log( z + sqrt(z*z-1.) );} 
                     else{return  I*log( z - sqrt(z*z-1.) );}}
             if(Re(z)>=0){return -I*log( z + sqrt(z*z-1.) );} 
                    else {return -I*log( z - sqrt(z*z-1.) );} }

 #define M(x,y) fprintf(o,"%6.4f %6.4f M\n",0.+x,0.+y);
 #define L(x,y) fprintf(o,"%6.4f %6.4f L\n",0.+x,0.+y);
 #define S(x,y) fprintf(o,"S\n",);

 main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d;
 FILE *o;o=fopen("acosplot.eps","w");ado(o,220,330);
 fprintf(o,"110 10 translate\n 100 100 scale\n");
 for(m=-1;m<2;m++){M(m,0)L(m,3)}
 for(n=0;n<4;n++){M(-1,n)L(1,n)}
 fprintf(o,"2 setlinecap .01 W 0 0 0 RGB S\n");
 DO(m,2001){ x=-1.+.001*m; z=x; y=Re(acos(z)); if(m==0)M(x,y) else L(x,y) }
 fprintf(o,"1 setlinejoin 1 setlinecap .02 W .5 0 0 RGB S\n"); p=1.8;q=.7;
 fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
       system("epstopdf acosplot.eps");
       system(    "open acosplot.pdf");
       getchar(); system("killall Preview");//for mac
 }

Latex generator of labels

 % Copyleft 2012 by Dmitrii Kouznetsov
 \documentclass[12pt]{article}
 \usepackage{geometry}
 \usepackage{graphicx}
 \usepackage{rotating}
 \paperwidth 432pt
 \paperheight 668pt
 \topmargin -90pt
 \oddsidemargin -80pt
 \textwidth 900pt
 \textheight 900pt
 \pagestyle {empty}
 \newcommand \sx {\scalebox}
 \newcommand \rot {\begin{rotate}}
 \newcommand \ero {\end{rotate}}
 \newcommand \ing {\includegraphics}
 \begin{document}
 \parindent 0pt
\sx{2}{ \begin{picture}(220,323)
 \put(4,6){\ing{acosplot}}
 \put(0,323){\sx{1.8}{$y$}}
 %\put(2,309){\sx{1.8}{$3$}}
 \put(0,210){\sx{1.8}{$2$}}
 \put(0,110){\sx{1.8}{$1$}}
 \put(0, 10){\sx{1.8}{$0$}}
 \put(1, 0){\sx{1.8}{$-\!1$}}
 \put(110, 0){\sx{1.8}{$0$}}
 \put(204, 0){\sx{1.9}{$x$}}
 \put(117,180){\sx{1.6}{\rot{-45}$y\!=\!\mathrm{acos}(x)$\ero}}
 \end{picture}
 }
 \end{document}

Keywords

«ArcCos», «Inverse function», «Explicit plot», «Elementary function»,