#include <stdio.h>

main() {
	float x, num, den, sig, sum;
	int n, i, j;

	printf("cos(x). Intro x y n : ");
	scanf("%f %d", &x, &n);
	sum = 0;
	for(i=0;i<=n;i++) {
		num = 1;
		for(j=1;j<=2*i;j++) {
			num = num *x;	// x^0=1; x^1=x; x^2=x*x;
		}
		den = 1;
		for(j=1;j<=2*i;j++) {
			den = den * j;	// 0!=1; 1!=1; 2!=2; 3!=6; 4!=24
		}
		sig = 1;
		for(j=1;j<=i;j++) {
			sig = sig*(-1);	// (-1)^0=1; (-1)^1=-1; (-1)^2=1
		}
		sum = sum + (num/den)*sig;
		printf("num=%.2f\tden=%.2f\tsig=%.2f\tsum=%f\n",num, den, sig, sum);
	}	
	printf("cos(%f)=%f\n", x, sum);
}