Mathc gnuplot/Application : Tangente de P à l'axes des x

/* ------------------------------------ */
/*  Save as :   c01.c                   */
/* ------------------------------------ */
#include "x_ahfile.h"
#include       "f2.h"
/* ------------------------------------ */
int main(void)
{
double c = .5;

 printf("  f : x-> %s  \n", feq);
 printf("  Df: x-> %s\n\n",Dfeq);

 printf(" With c = %0.3f, the equation of the tangent is :\n\n"
        "      y =  Df(c) (x-c) + f(c) = ",c);
 eq_Tan(c,f,Df);

 printf(" Find PA, the length of the tangent from P to the x axis.\n\n");

 printf(" P(%5.3f, %5.3f)           P(c, f(c))       \n",
        c,f(c));

 printf(" A(%5.3f, 0.000)           A(c-f(c)/Df(c), 0)\n\n\n",
          c-(f(c)/Df(c)));

 printf(" PA =  sqrt(f(c)**2*(1 +(1/Df(c)**2))) = %6.3f\n\n\n",
        sqrt(pow(f(c),2)*(1+(1/pow(Df(c),2)))));

 G_TanPx      (i_WGnuplot(-2,4,-1,2),
                 c,
               feq,f,Df);

 printf(" load \"a_main.plt\" with gnuplot. \n\n"
        " Press return to continue");
 getchar();

 return 0;
}

Le résultat.

 f : x->  cos(x)  
 Df: x->  (-sin(x)) 
.
With c = 0.500, the equation of the tangent is :
.
     y =  Df(c) (x-c) + f(c) =  -0.479*x +1.117
.
Find PA, the length of the tangent from P to the x axis.
.
P(0.500, 0.878)           P(c, f(c))       
A(2.330, 0.000)           A(c-f(c)/Df(c), 0)
.
PA =  sqrt(f(c)**2*(1 +(1/Df(c)**2))) =  2.030
.
load "a_main.plt" with gnuplot.

Résultat dans gnuplot

Les fichiers h de ce chapitre

	`x_ahfile.h` Appel des fichiers

/* ------------------------------------ */
/*  Save as :   x_ahfile.h              */
/* ------------------------------------ */
#include    <stdio.h>
#include   <stdlib.h>
#include    <ctype.h>
#include     <time.h>
#include     <math.h>
#include   <string.h>
/* ------------------------------------ */
#include     "xplt.h"
/* ------------------------------------ */
#include   "kg_tan.h"
#include    "k_tan.h"

	`f2.h` La fonction à dessiner

/* ------------------------------------ */
/*  Save as :   f2.h                    */
/* ------------ f --------------------- */
double f(
double x)
{
 return(       cos(x));
}
char  feq[] = " cos(x)";
/* ------------ f' ------------------- */
double Df(
double x)
{
 return(  (-sin(x)) );
}
char Dfeq[] = " (-sin(x)) ";

	`k_tan.h` Equation de la tangente

/* ------------------------------------ */
/*  Save as :    k_tan.h                */
/* ------------------------------------
   y = ax + b    [P(xp,yp);(y-yp)=a(x-xp)]


   a = f'(x)

   b = y - ax
   b = y - f'(x)x
   b = f(x) - f'(x)x

   x=c
   a = f'(c)
   b = f(c) - f'(c)c
   ------------------------------------ */
void eq_Tan(
double    c,
double (*P_f)(double x),
double (*PDf)(double x)
)
{
 printf(" %0.3f*x %+0.3f\n\n\n", 
 (*PDf)(c), (*P_f)(c) - (*PDf)(c)*c );
}
/* ------------------------------------ */
void eq_Tanf(
FILE *fp,
double    c,
double (*P_f)(double x),
double (*PDf)(double x)
)
{
fprintf(fp," %0.3f*x %+0.3f\n\n\n", 
 (*PDf)(c), (*P_f)(c) - (*PDf)(c)*c );
}

	`kg_tan.h` La fonction graphique

/* ------------------------------------ */
/*  Save as :   kg_tan.h                */
/* ------------------------------------ */
void G_TanPx(
W_Ctrl w,
double c,
  char    fEQ[],
double (*P_f)(double x),
double (*PDf)(double x)
)
{
FILE   *fp;

        fp = fopen("a_main.plt","w");   
fprintf(fp,"# Gnuplot file : load \"a_main.plt\" \n\n"
           " set zeroaxis \n"
           " plot [%0.3f:%0.3f] [%0.3f:%0.3f] \\\n"
           " %s,\\\n"
           " %0.6f*x %+0.6f,\\\n"
           " \"a_xaxe.plt\" with linesp lt 3 \n"
           " reset",
             w.xmini,w.xmaxi,w.ymini,w.ymaxi,
            fEQ,
       (*PDf)(c),-(*PDf)(c)*c+(*P_f)(c) );
 fclose(fp);

        fp = fopen("a_xaxe.plt","w");
fprintf(fp," %0.6f   %0.6f\n",c,(*P_f)(c) );
fprintf(fp," %0.6f   0.   \n",
c-((*P_f)(c)/(*PDf)(c)));
 fclose(fp);
}

Même exemple avec la fonction sin.

Résultat dans gnuplot