File:AsinplotT.png

Explicit plot of function ArcSin;

$y=\mathrm{arcsin}(x)$

is shown with dark blue line.

C++ geneator of curve

File ado.cin should be loaded to the working directory for 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.) );} }

z_type asin(z_type z){
if(Im(z)<0){if(Re(z)>=0){return M_PI/2.-I*log( z + sqrt(z*z-1.) );} 
                  else {return M_PI/2.-I*log( z - sqrt(z*z-1.) );}}
          if(Re(z)>=0){return M_PI/2.+I*log( z + sqrt(z*z-1.) );} 
                 else {return M_PI/2.+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("asinplot.eps","w");ado(o,220,330);
fprintf(o,"110 170 translate\n 100 100 scale\n");
for(m=-1;m<2;m++){M(m,-1.5)L(m,1.5)}
for(n=-1;n<2;n++){M(-1,n)L(1,n)}
 fprintf(o,"2 setlinecap .008 W 0 0 0 RGB S\n");
for(m=-1;m<2;m++){M(.5*m,-1.5)L(.5*m,1.5)}
DO(n,4){M(-1,-1.5+n)L(1,-1.5+n)}
fprintf(o,"2 setlinecap .005 W 0 0 0 RGB S\n");
DO(m,2001){ x=-1.+.001*m; z=x; y=Re(asin(z)); if(m==0)M(x,y) else L(x,y) }
fprintf(o,"1 setlinejoin 1 setlinecap .02 W 0 0 .6 RGB S\n"); p=1.8;q=.7;
fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
     system("epstopdf asinplot.eps");
     system(    "open asinplot.pdf");
     getchar(); system("killall Preview");//for mac
}

Latex generator of labels

The input file asinplot.pdf should be generated with the code above in order to compile the Latex document below.

% % Copyleft 2012 by Dmitrii Kouznetsov % <br> \documentclass[12pt]{article} % <br> \usepackage{geometry} % <br> \usepackage{graphicx} % <br> \usepackage{rotating} % <br> \paperwidth 432pt % <br> \paperheight 665pt % <br> \topmargin -90pt % <br> \oddsidemargin -80pt % <br> \textwidth 900pt % <br> \textheight 900pt % <br> \pagestyle {empty} % <br> \newcommand \sx {\scalebox} % <br> \newcommand \rot {\begin{rotate}} % <br> \newcommand \ero {\end{rotate}} % <br> \newcommand \ing {\includegraphics} % <br> \begin{document} % <br> \parindent 0pt \sx{2}{ \begin{picture}(220,321) % <br> \put(4,0){\ing{asinplot}} % <br> \put(2,320){\sx{1.7}{$y$}} % <br> \put(2,264){\sx{1.6}{$1$}} % <br> \put(2,164){\sx{1.6}{$0$}} % <br> \put(-6, 64){\sx{1.6}{$-\!1$}} % <br> \put(1, 0){\sx{1.6}{$-\!1$}} % <br> \put(44, 0){\sx{1.6}{$-\!0.5$}} % <br> \put(110, 0){\sx{1.6}{$0$}} % <br> \put(154, 0){\sx{1.6}{$0.5$}} % <br> \put(205, 0){\sx{1.7}{$x$}} % <br> \put(124,187){\sx{1.6}{\rot{48}$y\!=\!\mathrm{asin}(x)$\ero}} \end{picture} % <br> } % <br> \end{document}% <br> %

Keywords

ArcSin, ArcCos, Elementary function Inverse function