No idea for limit the sin(x) formula loop

Question

Making c/++ function to compute sin(x)

Referancing by the formula;

But i don't know where to stop infinity sum, and i don't want libraries for quick-answer. I want to make it. I made factorial function well. (fact() function)

double sin(int x) {
    int tp=0;
    for(int k=1; ;k++)
    {
        tp+=pow(-1,k)*pow(x,2*k+1)/fact(2*k+1);
    }
    return tp;
}

Answer 1

I ran the loop by 8 times, it's approaching to true value if you improve loop timing. Thanks @Sreeram TP

double sin(int x) {
    int tp=0;
    for(int k=1;k<8 ;k++)
    {
        tp+=pow(-1,k)*pow(x,2*k+1)/fact(2*k+1);
    }
    return tp;
}