#define _CRT_SECURE_NO_DEPRECATE
#include <stdio.h>
#include <math.h>
#include <locale.h>
#include <conio.h>

#define PI 3.1415926535

double taylor_sin(double x0, double prev, int step, int max) {
    double cur = -prev * x0*x0 / ((2 * step - 1)*(2 * step - 2));

    if (step < max)
        return cur + taylor_sin(x0, cur, ++step, max);

    else
        return cur;
}


double sin_t(double x0, int max) {
    return x0 + taylor_sin(x0, x0, 2, max);
}

int main()
{
    setlocale(LC_ALL, "rus");
    setlocale(LC_NUMERIC, "eng");

    printf("%lf", sin_t(PI, 10));

    _getch();
}