#include<iostream>
#include<math.h>

using namespace std;

long factorial(long N) {
    if (N < 2) return 1;
    for (int i = N - 1; i > 0; --i) {
        N = N * i;
    }
    return N;
}

double sin_taylor(double x, int N) {
    double res =  0;
    for (int k = 0; k < N; ++k) {
        res += pow(-1, k) * pow(x, 1 + 2*k) / (double)factorial(1 + 2*k);
    }
    return res;
}
void find_interval(int N) {
    for (double x = 0; x < 3.14; x += 0.00000001) {
        double real = sin(x);
        double taylor = sin_taylor(x, N);
        //cout << "Real: " << real << " Taylor: " << taylor << endl;
        if (abs(real - taylor) > 0.001) {
            cout << "Interval: [0, " << x - 0.01 << "]" << endl;
            break;
        }
    }
}

int main(int argc, char* argv[]) {
    find_interval(1);
    find_interval(2);
    find_interval(3);
    return 0;
}