Re{c} = Re{a}Re{b} - Im{a}Im{b}
    Im{c} = Re{a}Im{b} + Im{a}Re{b}

     /* trig1.c - Programme exemple par Don Cross  */
     /*           http://www.intersrv.com/~dcross/fasttrig.html         */

     #include <stdio.h>
     #include <math.h>

     #define PI (3.14159265358979323846)

     int main (void)
     {
            double a, da, a0_rad, da_rad;
            double a_sin, a_cos, da_sin, da_cos;
            double temp;
            int k;

            printf ( "Entrez l'angle de depart en degres: " );
            scanf ( "%lf", &a );
            a0_rad = a * PI / 180.0; /* convertit en radians */

            printf ( "Entrez l'increment angulaire en degres: " );
            scanf ( "%lf", &da );
            da_rad = da * PI / 180.0; /* convertit en radians */

            a_cos = cos(a0_rad);
            a_sin = sin(a0_rad);

            da_cos = cos(da_rad);
            da_sin = sin(da_rad);

            printf ( "\n%15s %15s %15s\n", "angle", "cosinus", "sinus" );
            printf ( "--------------- --------------- ---------------\n" );

            for ( k=0; k<20; k++ )
            {
                    printf ( "%15.5lf %15.7lf %15.7lf\n", a, a_cos, a_sin );

                    /* Voici le code qui met a jour les fonctions trigo... */

                    temp = a_cos*da_cos - a_sin*da_sin;
                    a_sin = a_cos*da_sin + a_sin*da_cos;
                    a_cos = temp;

                    /* Mettre a jour l'angle pour l'affichage. */
                    /* Cette etape n'a pas d'influence sur les fonctions trigo. */

                    a += da;
            }

            return 0;
     }

     /*--- fin du fichier trig1.c ---*/

     
     /* trig2.c - Programme exemple par Don Cross  */
     /*           http://www.intersrv.com/~dcross/fasttrig.html         */

     #include <stdio.h>
     #include <math.h>

     #define PI (3.14159265358979323846)

     int main (void)
     {
            double a, da, a0_rad, da_rad;
            double a_sin, a_cos, alpha, beta;
            double temp;
            int k;

            printf ( "Entrez l'angle de depart en degres: " );
            scanf ( "%lf", &a );
            a0_rad = a * PI / 180.0; /* convertit en radians */

            printf ( "Entrez l'increment angulaire en degres: " );
            scanf ( "%lf", &da );
            da_rad = da * PI / 180.0; /* convertit en radians */

            a_cos = cos(a0_rad);
            a_sin = sin(a0_rad);

            alpha = sin(0.5 * da_rad);
            alpha = 2.0 * alpha * alpha;

            beta = sin(da_rad);

            printf ( "\n%15s %15s %15s\n", "angle", "cosinus", "sinus" );
            printf ( "--------------- --------------- ---------------\n" );

            for ( k=0; k<20; k++ )
            {
                    printf ( "%15.5lf %15.7lf %15.7lf\n", a, a_cos, a_sin );

                    /* Voici le code qui met a jour les fonctions trigo... */

                    temp = a_cos - (alpha*a_cos + beta*a_sin);
                    a_sin = a_sin - (alpha*a_sin - beta*a_cos);
                    a_cos = temp;
                    
                   
                   /* Mettre a jour l'angle pour l'affichage. */
                    /* Cette etape n'a pas d'influence sur les fonctions trigo. */

                    a += da;
            }

            return 0;
     }

     /*--- fin du fichier trig2.c ---*/

exp(ix) = cos(x) + i sin(x)

z[n] = exp(i(nW + B))

     z[n+1] + z[n-1] 
     = exp(i(n+1)W + iB) + exp(i(n-1)W + iB) 
     = exp(inW + iW + iB) + exp(inW - iW + iB) 
     = exp(inW + iB) exp(iW) + exp(inW + iB) exp(-iW) 
     = z[n] exp(iW) + z[n] exp(-iW) 
     = z[n] (exp(iW) + exp(-iW)) 
     = z[n] (cos(W) + i sin(W) + cos(-W) + i sin(-W)) 
     = z[n] (cos(W) + i sin(W) + cos(W) - i sin(W)) 
     = 2 cos(W) z[n]

     z[n+1] + z[n-1] = 2 cos(W) z[n]

     z[n+1] = 2 cos(W) z[n] - z[n-1]

        #include <iomanip.h>
        #include <math.h>

        const double PI = 3.14159265358979323846;

        int main()
        {
               cout << "Entrez W en degres: " << flush;
               double w;
               cin >> w;
               w *= PI / 180.0; // convertit en radians

               cout << "Entrez B en degres: " << flush;
               double b;
               cin >> b;
               b *= PI / 180.0; // convertit en radians

               double y[3];
               y[0] = sin(-2*w + b);
               y[1] = sin(-w + b);
               const double p = 2.0 * cos(w);

               for ( int i=0; i<40; i++ )
               {
                       y[2] = p*y[1] - y[0];
                       y[0] = y[1];
                       y[1] = y[2];

                       cout << setprecision(10) << y[2] << endl;
               }

               return 0;
        }