如何编写一个程序来估计正弦函数作为 C 中的泰勒级数？

Question

I'm new to programming and I cannot figure out what is wrong with my code. If there is any way that someone could help me understand what is wrong with my program I would really appreciate it. I have already been working on this problem for two hours and I know I am making it harder than it needs to be. This is my new code. my new output is 0.000000476837158.

#include<stdio.h>
#include<stdlib.h>
#include<math.h>
int main() {
         double x, sinx, z, factorial, term;
         int j, n, i;
         x=0.5;
         n=10;
         i=0;
         z=sin(0.5);
         for(int i=0; i<=n; i++){
                      factorial = 1;
                      for(j=2*i +1; j<=i; j++)
                      {
                               factorial = factorial * j;
                               }
                      term=(pow(-1,i)*pow(x,2*i+1))/(factorial);
                      sinx=term++;
                      i=i++;
                                   }
                      printf("sin(0.5) is approximately %.15lf\n", sinx);
                      printf("sin(0.5) by default function is %.15lf\n", z);
                      system("pause");
                      return 0;
                      }

Answer 1

This loop doesn't make sense.

 for(j=0; j<=i; j++){
     factorial=2*j+1;
     }

It doesn't do anything different than

factorial = 2*i+1;

If you wanted to calculate a factorial(like i! ) than I'd do the following

// initialize `factorial`
factorial = 1;
for(j=1; j<=i; j++)
{
    //multiply `factorial` by `j`.  
    factorial = factorial * j;
}

---

you keep using sinx and term , but they're never initialized. This means that they'll contain garbage values.

---

i++ incriments on it's own, you shouldn't have to use any extra assignment operators.

change

i=i++;

to simply

i++;

or better yet, use a for loop instead of a while loop

for(int i=0; i<=n; i++)

Answer 2

The first occurrence of this statement

     sinx=sinx+term;

will be one of your problems since neither of the variables on the rhs of the assignment has been initialised when you first use them. Subsequent executions of the same line, inside the loop, will propagate the junk value of sinx throughout the computation.

I expect there are other problems too but haven't examined the code very closely.

Answer 3

Your i ^th term is -1 ⁱ x ²ⁱ⁺¹ /i, which grows fast . You should have printed out the first couple of terms to discover the problem.

(There are other problems too, like i=i++; , but they can wait.)