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

// z_1 = cos(3pi / 8 - alpha / 4)^2 - cos(11pi / 8 + alpha / 4)^2
// z_2 = sqrt(2) / 2 * sin(alpha / 2)

int main() {
    double alpha = 0, z_1 = 0, z_2 = 0;

    printf("Input Ɑ: ");

    if (scanf("%lf", &alpha) != 1){
        printf("\e[1;31m[ERROR] Alpha must be a double, restart the program.\n\e[0m");
        return 0;
    }

    z_1 = cos(3 * M_PI / 8 - alpha / 4) * cos(3 * M_PI / 8 - alpha / 4) - cos(11 * M_PI / 8 + alpha / 4) * cos(11 * M_PI / 8 + alpha / 4);
    z_2 = sqrt(2) / 2 * sin(alpha / 2);

    printf("z_1 = %lf\n", z_1);
    printf("z_2 = %lf\n", z_2);

    return 0;
}