File:SazaeconT.png

Graphics of functions Cohc and Cosc. Meanings of constants Sazae, Tarao, Fune, Wakame.


 * $ \displaystyle \mathrm{cosc}(z)=\frac{\cos(z)}{z} ~,$ $~ ~ \displaystyle \mathrm{cohc}(z)=\frac{\cosh(z)}{z} ~,$

C++ generator of curves
File ado.cin should be stored in 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<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"

main{ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; //DB y1 = 1.1996786402577337; DB Sazae= 2.798386045783887; DB Tarao=-0.33650841691839534; DB Ho   =1.199678640257734; DB Fune =1.199678640257734; DB Jo   =1.50887956153832; DB Wakame=1.50887956153832; FILE *o;o=fopen("sazaecon.eps","w");ado(o,520,430); fprintf(o,"10 110 translate\n 100 100 scale\n"); for(m=0;m<6;m++){M(m,-1)L(m,3)} for(n=-1;n<4;n++){M(0,n)L(5,n)} fprintf(o,"2 setlinecap .006 W 0 0 0 RGB S\n");
 * 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",);

DO(m,291){ x=.336+.01*m; y=cosh(x)/x; if(m==0)M(x,y) else L(x,y) } fprintf(o,"1 setlinejoin 1 setlinecap .02 W 0 .8 0 RGB S\n"); M(Fune,0)L(Fune,Wakame)L(0,Wakame) fprintf(o,"2 setlinecap .003 W 0 0 0 RGB S\n"); DO(m,476){ x=.31+.01*m; y=cos(x)/x; if(m==0)M(x,y) else L(x,y) } fprintf(o,"1 setlinejoin 1 setlinecap .02 W .9 0 0 RGB S\n"); p=1.8;q=.7; M(Sazae,0)L(Sazae,Tarao)L(0,Tarao) M( .5*M_PI,-.1)L( .5*M_PI,.1) M(1.5*M_PI,-.1)L(1.5*M_PI,.1) fprintf(o,"2 setlinecap .003 W 0 0 0 RGB S\n"); fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o); system("epstopdf sazaecon.eps"); system(   "open sazaecon.pdf"); getchar; system("killall Preview");//for mac }

Latex generator of labels
File sazaecon.pdf should be generated with the code above (and stored in the working directory) in order to compile the Latex dovument below.

% % Copyleft 2012 by Dmitrii Kouznetsov % \documentclass[12pt]{article} % \usepackage{geometry} % \usepackage{graphicx} % \usepackage{rotating} % \paperwidth 1020pt % \paperheight 810pt % \topmargin -90pt % \oddsidemargin -106pt % \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}(540,410) % %\put(4,6){\ing{acosplot}} % % \put(4,6){\ing{aciplot}} % % \put(4,6){\ing{cohcplot}} % \put(4,6){\ing{sazaecon}} % \put(16,402){\sx{2.5}{$y$}} % \put(16,309){\sx{2.2}{\bf 2}} % \put(16,209){\sx{2.2}{\bf 1}} % %\put(16,160){\sx{1.8}{\bf 2.5}} % \put(16, 262){\sx{2.2}{Wakame}} % \put(16,109){\sx{2.2}{\bf 0}} % \put(16, 75){\sx{2.4}{Tarao}} % \put(107, 120){\sx{2.2}{\bf 1}} % \put(142,120){\sx{2.4}{\rot{90}Fune\ero}} % \put(207, 120){\sx{2.2}{\bf 2}} % \put(302,118){\sx{2.5}{\rot{90}Sazae\ero}} % \put(307, 120){\sx{2.2}{\bf 3}} % \put(407, 120){\sx{2.2}{\bf 4}} % \put(161, 132){\sx{2.8}{$\frac{\pi}{2}$}} % \put(471, 130){\sx{2.6}{$\frac{3\pi}{2}$}} % \put(508, 126){\sx{2.4}{$x$}} % \put(224,282){\sx{2.5}{\rot{48}$y\!=\!\mathrm{cohc}(x)$\ero}} % \put(317, 66){\sx{2.6}{\rot{7}$y\!=\!\mathrm{cosc}(x)$\ero}} % \end{picture} % } % \end{document} %

Keywords
Cohc, ArcCohc, Cosc, ArcCosc, Sazae, Tarao, Fune, Wakame