Mathc initiation/Fichiers c : c77ur

Sommaire

Installer et compiler ces fichiers dans votre répertoire de travail.

	c1u.c

/* --------------------------------- */
/* save as c1u.c                     */
/* --------------------------------- */
#include "x_hfile.h"
#include      "fu.h"
/* --------------------------------- */
int main(void)
{
double x  = 1.2;

 clrscrn();
 
 printf("  x =  %0.1f  \n\n\n",x);
 
 printf("  %s \t\t\t\t\t= %0.8f\n",  f1eq, f1(x));
 printf("  %s \t= %0.8f\n\n\n",    f2eq, f2(x));
 

 stop();

 return 0;
}
/* ---------------------------------- */
/* ---------------------------------- */

Vérifions par le calcul :

  x =  1.2  


  tan(3.*x) 				            	= 0.49346673
  (3tan(x) -tan(x)**3) / (1-3tan(x)**2) 	= 0.49346673


 Press return to continue.

Vérifions les égalités :

    Nous avons vu que :
    
                             tan(y) +  tan(x)
                 tan(y+x)  = ----------------     
                             1 - tan(y)tan(x)
                                                       
     
    posons y = 2x :     
    
                             tan(2x) +  tan(x)    
                 tan(2x+x) = ----------------     
                             1 - tan(2x)tan(x)     
                             

                             tan(2x) +  tan(x)    (a)
                  tan(3x)  = ----------------     
                             1 - tan(2x)tan(x)    (b)
                              
 a) ------------------------------------------
 
                          2tan(x)
    tan(2x) +  tan(x) = ----------- +  tan(x)                        
                        1-tan(x)**2
                          
                          
                          2tan(x)      tan(x)  (1-tan(x)**2)
                      = ----------- +  ---------------------                        
                        1-tan(x)**2       1-tan(x)**2
                        
                                
                          2tan(x)      tan(x)-tan(x)**3
                      = ----------- +  ----------------                       
                        1-tan(x)**2      1-tan(x)**2
                                      
                                      
                          3tan(x) -tan(x)**3
                      = --------------------                      
                            1-tan(x)**2 
                            
                            
  b) ------------------------------------------       
  
                             2tan(x)
  1 - tan(2x)tan(x) =  1 - -----------  tan(x)
                           1-tan(x)**2
  
                       1-tan(x)**2   2tan(x)**2
                    =  ----------- - ----------- 
                       1-tan(x)**2   1-tan(x)**2    
                           
                       1-3tan(x)**2   
                    =  ------------     
                        1-tan(x)**2        
                           
                           
 a/b) ------------------------------------------                            
                           
                           
                          3tan(x) -tan(x)**3
                          ------------------                      
                            1-tan(x)**2                            
            tan(3x ) = ------------------------  
                            1-3tan(x)**2   
                            ------------     
                            1-tan(x)**2                                
                           
  donc                          
                           
                       3tan(x) -tan(x)**3    
            tan(3x ) = ------------------                         
                          1-3tan(x)**2