Calculate the function sin()

Question

For my studies, I have to code an algorithm to calculate sin() with this function:

Answer 1

Idea about the number of terms with OP's posted answer.

As long as one performs some range limitation first, like fmod(), the number of terms needed can be reasonably determined dynamically. (Uses 1 to 23 iterations for x: 0 to 2*pi.)

double sinX1(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)
    for(i = 2; ((1.0 + term_i) != 1.0); i+=2)
    {
        term_i = (-term_i * (x*x)) / (i*(i+1));
        result += term_i;
    }
    return x * result;
}