Finally, I followed yours indications. Here is my final code :
double sinX(double x)
{
double result = 1.0;
double term_i = 1.0;
int i = 2;
x = fmod(x, 2*M_PI);
for(i = 2; i<= 30; i+=2)
{
term_i = (-term_i * (x*x)) / (i*(i+1));
result += term_i;
}
return x * result;
}