#define _USE_MATH_DEFINES
#include <iostream>
#include <fstream>
#include <vector>
#include <string>
#include <sstream>
#include <iomanip>
#include <cmath>
#include <math.h>
#define  prt(x) cout << x << endl
using namespace std;

double h = 0.05;
double x0 = M_PI / 6;

double f(double x) {
	return pow(sin(x), 2);
}


int main() {
	system("color F2");
	ifstream fin("in.txt");
	ofstream fout("res.txt");

	double f1_x0 = (f(x0 + h) - f(x0 - h)) / (2 * h);
	prt(f1_x0);

	double f1_x0_t = (8 * (f(x0 + h) - f(x0 - h)) + f(x0 - 2 * h) - f(x0 + 2 * h))
					/ (12 * h);
	prt(f1_x0_t);
	prt(sin(2 * x0));
	prt("");

	double f2_x0 = (f(x0 + h) + f(x0 - h) - 2 * f(x0)) / (h* h);
	prt(f2_x0);

	double f2_x0_t =	(16 * (f(x0 + h) + f(x0 - h))
						- 30 * f(x0)
						- f(x0 + 2 * h) - f(x0 - 2 * h)) / (12 * h* h);
	prt(f2_x0_t);

	prt(2 * cos(2 * x0));
	system("pause");
	return 0;
}