BdMO Online Forum

Code: Select all

double sin(double x) {
    double res = 0;
    int sign = 1;
    double denom = 1;
    double num = x;
    for(i = 1; i <= 100; i+=2) {
        res += (sign * num) / denom;
        num *= (x*x);
        denom *= ((i+1)*(i+2));
        sign *= -1;
    }
    return res;
}

Code: Select all

//we will write a function to calculate sine of a given value
//we will use MacLaurin Series for this purpose
//sinx = x - x^3 / 3! + x^5 / 5! - ......
double sin(double x) {
    double res = 0; //result variable
    int sign = 1; //sign of a particular term in the series, +/-
    double num = x; //num variable will denote the numerator of a particular term in the series
    double denom = 1; //denom variable will denote the denominator of a particular term in the series

    //it's not possible to calculate a infinite sum
    //it's not necessary either because later terms won't contribute much to the sum
    //so we will take first 50 odd terms
    for(int i = 1; i <= 100; i+=2) {
        res += (sign * num) / denom; // 'res += x' means 'res = res + x'
        num *= (x*x); //next numerator, note that each term is x^2 more than the previous one
        denom *= ((i+1)*(i+2)); //next denominator, note that i-th term should be (2*i+1)!
        sign *= -1; //sign alternates in successive terms
    }
    return res;
}

Code: Select all

double factorial(int n) {
    double res = 1;
    for(int i = 1; i <=n; i++) {
        res = res * n;
    }
    return res;
}

double sin(double x) {
    double res = 0;
    int sign = 1;
    for(i = 1; i <= 100; i+=2) {
        double num = pow(x, i);
        double denom = factorial(i);
        res = res + ((sign * num) / denom);
        sign *= -1;
    }
    return res;
}