Question

The standard math library provides a Complex functions such as these are usually approximated using some numeric analy technique. One such technique is to use a Taylor series to approximate the sine function function to compute the sine of a given number i-0 Obviously, we cannot compute an infinite series. Instead, we will approximate sin(z) by computing the Taylor series above out to n terms We have provided you with an incomplete program, sine.c that reads in two values from the command line, x and n. We have also written a function to compute the factorial which you may find useful. You will need to complete the program by writing code to compute the approximation of sin(r)

This is the given code:

/**
* This program uses a Taylor Series to compute a value
* of sine.
*
*/
#include<stdlib.h>
#include<stdio.h>
#include<math.h>

/**
* A function to compute the factorial function, n!.
*/
long factorial(int n) {
long result = 1, i;
for(i=2; i<=n; i++) {
result *= i;
}
return result;
}

int main(int argc, char **argv) {

if(argc != 3) {
fprintf(stderr, "Usage: %s x n ", argv[0]);
exit(1);
}

double x = atof(argv[1]);
int n = atoi(argv[2]);

double result = 0.0;

//compute sin(x) using a taylor series out to n terms

printf("sin(%f) = %f ", x, result);

return 0;
}

How would you solve this?

Answer 1

EXPECTED ANSWER

//Program

#include<math.h>
#include<stdio.h>
int main()
{
double sum=0.00,num,s;
long x,i,n,den,f;
printf(" Enter the value of x: "); //sin(4)
scanf("%ld",&x);
printf(" Enter the value of n: ");
scanf("%ld",&n);
for(i=0;i<=n;i++)
   {
   den=2*i+1;
   num=pow(x,den);
   f=1;
   while(den!=0)
       {
       f=f*den;den--;
       }
   sum=sum+(num*pow(-1,i))/f;
   }
printf(" The taylor series approximation of sin(%ld) is : %lf",x,sum);
s=sin(x);
printf(" The Math library function aroximation of sin(%ld) is : %lf",x,s);
printf(" The error os %lf",sum-s);
return 0;
}

sample run

THANK YOU ....!

囲DOSBox 0.74, Cpu speed: max 100% cycles, Frameskip 0, Program: TC CNTURBOC3 BIN>exit mter the value of x: 4 Enter the value of n: 4 The taylor series approximation of sin(4) is0.661728 The Math library function aroximation of sin(4) is : -0.756802 The error os 0.095074 Enter the value of x: 5 Enter the value of n 5 The taylor series approximation of sinc5) is1.133617 The Math library function aroximation of sin(5) is0.958924 The error os -0.174693 Math ibrary function aroxinat ion of sint5) is;