File:Ausinplot1.jpg

Explicit plot of function AuSin for real values of the argument.

$y=\mathrm{AuSin}(z)$

Additional grid lines $x\!=\!\pi/2$ and $x\!=\!\pi$ are drawn.

C++ generator of curves
Files ado.cin, arcsin.cin, susin.cin, ausin.cin should be loaded to the working directory

using namespace std; typedef complex z_type;
 * 1) include 
 * 2) include 
 * 3) include 
 * 4) define DB double
 * 5) define DO(x,y) for(x=0;x<y;x++)
 * 1) include
 * 1) define Re(x) x.real
 * 2) define Im(x) x.imag
 * 3) define I z_type(0.,1.)


 * 1) include "ado.cin"
 * 2) include "arcsin.cin"
 * 3) include "susin.cin"
 * 4) include "ausin.cin"

int main{ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; FILE *o;o=fopen("ausinplo.eps","w"); ado(o,318,420); fprintf(o,"1 1 translate\n 100 100 scale\n"); fprintf(o,"1 setlinejoin 2 setlinecap\n"); for(m=0;m<4;m++){M(m,-1) L(m,4) } for(n=0;n<5;n++){M( 0,n) L(M_PI,n)} fprintf(o,".006 W 0 0 0 RGB S\n"); M(M_PI/2.,0); L(M_PI/2.,4) M(M_PI,0); L(M_PI,4) fprintf(o,".004 W 0 0 0 RGB S\n"); fprintf(o,"1 setlinejoin 1 setlinecap\n"); DO(m,201){ x=M_PI/2.+.009*(m-100); z=z_type(x,1.e-8); c=ausin(z); y=Re(c); if(m==0)M(x,y) else L(x,y); printf("%8.5f %8.5f\n",x,y); } fprintf(o,".03 W 0 0 .8 RGB S\n"); /* DO(m,100){ x=.5+.1*m; y=sqrt(3./x); if(m==0) M(x,y) else L(x,y) ; if ( x>10.) break;} fprintf(o,".01 W 0 0 0 RGB S\n"); //n=0;DO(m,100){ x=.1*m; z=z_type(x,1.e-8); c=susin(z); y=Im(c); if(y>-2 && y<3) { if(n==0) M(x,y) else L(x,y); n++;}} //fprintf(o,".02 W .8 0 0 RGB S\n"); printf("n=%3d\n",n); fprintf(o,"showpage\n"); fprintf(o,"%c%cTrailer\n",'%','%'); fclose(o); system("epstopdf ausinplo.eps"); system( "open ausinplo.pdf"); //for macintosh getchar; system("killall Preview"); // For macintosh }
 * 1) define M(x,y) {fprintf(o,"%6.4f %6.4f M\n",0.+x,0.+y);}
 * 2) define L(x,y) {fprintf(o,"%6.4f %6.4f L\n",0.+x,0.+y);}

Latex generator of labels
\documentclass[12pt]{article} \usepackage{geometry} \usepackage{graphics} \paperwidth 332pt \paperheight 438pt \topmargin -109pt \oddsidemargin -90pt

\newcommand \sx {\scalebox} \pagestyle{empty} \begin{document} \begin{picture}(320,432) \put(14,16){\includegraphics{ausinplo}} \put(1,420){\sx{2.2}{$y$}} %\put(-1,151){\sx{2.8}{$\frac{\pi}{2}$}} \put(0,308){\sx{2.2}{$3$}} \put(0,208){\sx{2.2}{$2$}} \put(0,108){\sx{2.2}{$1$}} \put(0,8){\sx{2.2}{$0$}} \put(10,-4){\sx{2.2}{$0$}} \put(110,-4){\sx{2.2}{$1$}} \put(151,-4){\sx{2.1}{$\pi/2$}} \put(210,-4){\sx{2.2}{$2$}} \put(320,-3){\sx{2.2}{$x$}} %\put(140,166){\sx{2.8}{$y\!=\! \sqrt{3/x}$}} %\put(135,56){\sx{2.8}{$y\!=\!\mathrm{SuSin}(x)$}} \end{picture} \end{document}