Question

The cosine function is analytically defined as follows: m 1. x² + x6 (-1)" x2m COS X = (-1)" x2n (2n)! 2!*4!- 6 + ... + (2m)! Write a complete C program that has three functions: main, cosine, and factorial. The cosine function receives a real number x and returns a real number representing the cosine of x. The cosine function also receives another integer m that determines the number of terms that will be used in computing the cosine value. The integer m is input from the user (Assume that m>0). The factorial function receives an integer n and returns the factorial n!, which is also an integer. n!- 1*2*3*......* (n-1)*n Note: You are not allowed to use cos(x) from the library math.h. -No call to printf or scanf inside cos and factorial functions. - Put the definition of cos and factorial functions after the definition of the main function. The following is a sample run of the program: Enter x: 0.5 Enter m: 10 Result: 0.877583

Answer 1

CODE

#include<stdio.h>
#include<math.h> //to use pow function

int fact(int n) {
   if(n==0)
       return 1;
   else
       return n*fact(n-1);
}

double cosValue(double x, int m) {
   double sum = 0;
   int i;
   for(i=0;i<=m;i++)
           sum += (pow(-1, i) * pow(x, 2*i))/fact(2*i);
  
   return sum;
}

int main() {
   int m;
   double x;
   printf("Enter x: ");
   scanf("%lf", &x);
  
   printf("\nEnter m: ");
   scanf("%d", &m);
  
   printf("\nResult: %lf", cosValue(x, m));
  
}

OUTPUT

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