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:

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=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.) );} }

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 }
 * 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));
 * 3) define S(x,y) fprintf(o,"S\n",);

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 % \documentclass[12pt]{article} % \usepackage{geometry} % \usepackage{graphicx} % \usepackage{rotating} % \paperwidth 432pt % \paperheight 665pt % \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}(220,321) % \put(4,0){\ing{asinplot}} % \put(2,320){\sx{1.7}{$y$}} % \put(2,264){\sx{1.6}{$1$}} % \put(2,164){\sx{1.6}{$0$}} % \put(-6, 64){\sx{1.6}{$-\!1$}} % \put(1, 0){\sx{1.6}{$-\!1$}} % \put(44, 0){\sx{1.6}{$-\!0.5$}} % \put(110, 0){\sx{1.6}{$0$}} % \put(154, 0){\sx{1.6}{$0.5$}} % \put(205, 0){\sx{1.7}{$x$}} % \put(124,187){\sx{1.6}{\rot{48}$y\!=\!\mathrm{asin}(x)$\ero}} \end{picture} % } % \end{document}% %

Keywords
ArcSin, ArcCos, Elementary function Inverse function