find the value of cos(x) using the series

/* Write a C program to find the value of cos(x) using the series *
* up to the given accuracy (without using user defined function) *
* Also print cos(x) using library function. */

#include stdio.h
#include conio.h
#include math.h
#include stdlib.h

void main()
{
int n, x1;
float acc, term, den, x, cosx=0, cosval;

clrscr();

printf("Enter the value of x (in degrees)\n");
scanf("%f",&x);

x1 = x;

/* Converting degrees to radians*/

x = x*(3.142/180.0);
cosval = cos(x);

printf("Enter the accuary for the result\n");
scanf("%f", &acc);
term = 1;
cosx = term;
n = 1;

do
{
den = 2*n*(2*n-1);
term = -term * x * x / den;
cosx = cosx + term;
n = n + 1;
} while(acc <= fabs(cosval - cosx)); printf("Sum of the cosine series = %f\n", cosx); printf("Using Library function cos(%d) = %f\n", x1,cos(x)); } /*End of main() */ /*------------------------------ Output Enter the value of x (in degrees) 30 Enter the accuary for the result 0.000001 Sum of the cosine series = 0.865991 Using Library function cos(30) = 0.865991 RUN 2 Enter the value of x (in degrees) 45 Enter the accuary for the result 0.0001 Sum of the cosine series = 0.707031 Using Library function cos(45) = 0.707035 ---------------------------------------------*/

This program is completly same as previous program. Same explanation. Insted we use the cosine taylor formula here

Hence we have the series

x² x⁴ x⁶ x⁸

1 - + - + - ...

2! 4! 6! 8!

Notice that the series only contains even powers of x and even factorials. Even numbers can be represented by 2n. Also notice that this is an alternating series, hence the McLaurin series is