#include <stdio.h>
#include <math.h>

double sin0(double x);
double sin1(double x);

static const double PI = 3.14159265358979323846;
static const double EPS = 1e-9;

int main() {
    while (true) {
        double x;
        printf("x: ");
        if (scanf("%lf", &x) < 1)
            break;
        printf(
            "sin0(x) = %.8lf, sin1(x) = %.8lf\n",
            sin0(x), sin1(x)
        );
        printf("Test: standard sin(x) = %.8lf\n", sin(x));
    }
    return 0;
}

// Compute sin(x) as a sum of Taylor series
double sin0(double x) {
    // sin(x) = x - x^3 / 3! + x^5 / 5! - x^7 / 7! + ...
    double s = 0.;
    double r = x;;
    double n = 1.;
    while (fabs(r) >= EPS) {
        s += r;
        r *= -x*x/((n+1.)*(n+2.));
        n += 2.;
    }
    return s;
}

// Reduce an argument of sin to the interval [-PI, PI]
// before computing of the Taylor series,
// using the periodicity of sin
double sin1(double x) {
    x = fmod(x, 2.*PI);
    if (x > PI)
        x -= 2.*PI;
    else if (x < -PI)
        x += 2.*PI;
    return sin0(x);
}