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// cos(x) = Somme(n=0, +oo) (-1)^n . (x^{2n}) / (2n)!
double calculerCos(double X,double precision)
{
double terme_1 = 1; // (-1)^n
double terme_2 = 1; // x^{2n}
double terme_3 = 1; // 1/(2n)!
double terme_final = 1; // (-1)^n . (x^{2n}) / (2n)!
double reponse = 1;
long int n = 0;
do
{
terme_1 *= (-1);
terme_2 *= (X * X);
/* Somme(n=0, +oo) = 1/1 + 1/(1*2) + 1/(1*2*3*4) + 1/(1*2*3*4*5*6 + ...
on a donc T(k) = T(k- 1).1/((n + 1)(n +2)) avec n = 0 si k = 0 et n est
incrémenté de 2 à chaque itération
*/
terme_3 *= 1/((double)(n + 1)*(n + 2));
terme_final = (terme_1 * terme_2 * terme_3);
reponse +=terme_final;
n+= 2;
}while (abs(terme_final) > precision);
return reponse;
}
// sin(x) = Somme(n=0, +oo) (-1)^n . (x^{2n + 1}) / (2n +1)!
double calculerSin(double X,double precision)
{
double terme_1 = 1; // (-1)^n
double terme_2 = X; // x^{2n +1}
double terme_3 = 1; // 1/(2n + 1)!
double terme_final = 1; // (-1)^n . (x^{2n + 1}) / (2n +1)!
double reponse = X;
long int n = 1;
do
{
terme_1 *= (-1);
terme_2 *= (X * X);
/* Somme(n=0, +oo) = 1/1 + 1/(1*2) + 1/(1*2*3*4) + 1/(1*2*3*4*5*6 + ...
on a donc T(k) = T(k- 1).1/((n + 1)(n +2)) avec n = 0 si k = 0 et n est
incrémenté de 2 à chaque itération
*/
terme_3 *= 1/((double)(n + 1)*(n + 2));
terme_final = (terme_1 * terme_2 * terme_3);
reponse +=terme_final;
n+= 2;
}while (abs(terme_final) > precision);
return reponse; |
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