namespace myfuncs {
    const double PI2 = M_PI * 2;
    // calculate sin using taylor series
    // D(y) = R
    double sin(double x) {
        while (abs(x) > PI2) {
            x += x > 0 ? -PI2 : PI2;
        }
        double result = 0;
        double term = x;
        int i = 1;
        while (term != 0) {
            result += term;
            term *= -1 * x * x / (2 * i * (2 * i + 1));
            i++;
        }
        return result;
    }

    // calculate cos using taylor series
    // D(y) = R
    double cos(double x) {
        while (abs(x) > PI2) {
            x += x > 0 ? -PI2 : PI2;
        }
        double result = 0;
        double term = 1;
        int i = 1;
        while (term != 0) {
            result += term;
            term *= -1 * x * x / (2 * i * (2 * i - 1));
            i++;
        }
        return result;
    }

    // calculate pow
    double pow(double x, double y) {
        double result = 1;
        if (y == 0) {
            return 1;
        }
        if (y < 0) {
            x = 1 / x;
            y = -y;
        }
        while (y > 0) {
            result *= x;
            y--;
        }
        return result;
    }
}