C Program to compute the cosine series using function. =1-x2/2!+x4/4!-x6/6!----
Objective
Write a C program to compute the Cosine series: 1 - x2/2! + x4/4! - x6/6!...
Algorithm / Approach
- Create a
cal_cos(x, n)function. - Inside it, use a loop to iterate
ntimes. - Use the condition
if (i % 2 == 0)to alternate between adding and subtracting the term from the sum. - The term formula is
pow(a, j) / fact(j), wherejstarts at 2 and increments.
main.c
#include<stdio.h>
#include<math.h>
float cal_cos(int, int);
int fact(int);
int main( )
{
int x, n;
printf("Enter the value of x : ");
scanf("%d",&x);
printf("Enter the value of n : ");
scanf("%d",&n);
float r = cal_cos(x, n);
printf("Result = %f ",r);
return 0;
}
float cal_cos(int a, int n) {
int j =2 ;
float sum = 1;
for(i=1; i<=n; i++)
{
if(i%2 ==0)
{
sum = sum+pow(a,j)/(float)fact(j);
}
else
{
sum = sum-pow(a,j)/fact(j);
}
}
return sum;
}
int fact(int x){
int i, f=1;
for(i=1; i<=x; i++){
f = f*i;
}
return f;
}Expected Output
Enter the Value of x : 3 Enter the Value of n : 3 Result = -1.250000
Explanation of the Program
- The Cosine series (a Maclaurin series in calculus) calculates the exact value of a cosine angle using infinite polynomials.
- Notice the explicit cast
(float)fact(j). Becausepow()andfact()both return integers in this specific code, dividing them would cause integer truncation. Casting forces floating-point division to preserve decimal accuracy.
Complexity
Time Complexity
O(n^2)
Space Complexity
O(1)
