/* Cosine Series - Program to find cos(x) using the series: cos(x) = 1 - (x^2) / 2! + (x^4) / 4! - (x^6) / 6! + .... Do calculations till the value of the next term is not lesser than 10^-5  */

/* We assume that the angle entered by user is between 0 and 2 pi radians (0 and 360 degrees) */

#include  <stdio.h>
#include  <conio.h>
#define  pi  3.141593

void main()
{
    double  d, x, i=0, s=0, f=1, num, nt;
    int  tc=1 ;
    /* s-sum , f-factorial , num - nemerator , nt - next term , tc - term count */
    clrscr() ;
    printf("Enter the angle in degrees: ") ;
    scanf("%lf", &d) ;
    x=d*pi/180 ; /* converts angle to radians */
    num=1 ;
    while(1)
        {
            f=f*i*(i-1) ;  /* Calculates factorial */
            if(f==0)
                f=1 ;
            nt=num/f ;      /* calculates next term */
            if(nt<0.00001)
                break  ;  /* stops if next term is less than 10 raise to -5 */
            if(tc%2==1)  /* alternating + and - */
                s=s+nt ;        /* calculates sum*/
            else
                s=s-nt ;
            /* Preparation for next execution */
            i=i+2 ;
            tc++ ;
            num=num*x*x ;
        }
    printf("The cosine of angle %lf is %lf", d, s) ;
    getch() ;
}

/*
Output

Enter the angle in degrees: 60
The cosine of angle 60.000000 is 0.500000
*/