Sine series equation not calculating properly

Question

I can't find the logic error in my code. is the entire thing wrong mathematically? or is it partially correct.

float x,term,fx;
int i, nterms;
cin>>x>>nterms;
for(i=1;i<=nterms;i+=2){ 
term=1;
fact=1;
for(j=1;j<=i;j++){
        term=term*x;
        fact=fact*j;
}
sign=-1*sign;
fx+=sign*term/fact;
}

cout << fixed << showpoint;
cout << setprecision(6);
cout<<fx;

Answer 1

I fixed your code step by step, I can't go further because I'm not sure what you want to do in your code. If you tell us what they are, I'll be able to fix this code.

#include <iostream>
#include <iomanip>
#include <stdio.h>

int main() {
  long double x,term,fx, fact;
  int i, j, nterms;
  int sign;

  std::cin>>x>>nterms;
  term=1;
  fact=1;
  sign=1;
  fx = 0;
  for(i=1;i<=nterms;i+=2){ 
    for(j=1;j<=i;j++){
      term=term*x;
      fact=fact*j;
    }
    sign=-1*sign;
    fx+=sign*term/fact;
  }
  std::cout << std::setprecision( 6 )  << fx << std::endl;
}

Some remarks here:

1. It seems that using namespace was used for std. Use it carefully, since a conflict between some namespaces could occur. This page (french) suggest two use case.

   a. Importing the symbols one by one:

   using std::cout; 
   using std::endl; 
   

   b. Use them only in a local scope (in a curly brace block for example):

   void a_function() { 
       // std will be imported only within this block 
       using namespace std;   
      cout << "hello there" << endl; // will work
   }
   

2. Declare your variables before using them. Compare my answer with your code sample.

3. Be careful with the min and max values a type can handle. Your function seems to handle very huge or small values. I changed their type to long double (but it's just moving the issue further). You have the ranges. Have a look this SO answer. It leads to limit.h, which shows numeric limits. Pick the safest to store your values (or sets a max and min value for user inputs).