c - Is this flowchart right?

Question

I've developed a C program that can calculate the value of a sin function using Taylor series expansion. I've also drawn a flowchart for the program. The source code is given below:

#include<stdio.h>
#include<math.h>

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

int main()
{
 int l,i,t=1;
 float deg,rad,val=0;

 printf("Enter degree of sin: ");
 scanf("%f",&deg);

 printf("Enter limit of Taylor series: ");  
 scanf("%d",&l);                            
 rad = (deg*3.142857)/180;                  

 for(i=1;i<=l;i+=2)
  {
   val = val + (t*pow(rad,i)/fact(i));     
   t = t*(-1);                         
  }

 printf("
Value calculated by program, using Taylor Series:
");
 printf("Sin(%f) = %f
",deg,val);
 printf("
Value calculated using library function:
");
 printf("Sin(%f) = %f
",deg,sin(rad));

 getch();
 return 0;
}

And here's the flowchart for the program:

So is this flowchart right for the program? Are there any mistakes? I am a fresher in programming and don't have a good knowledge in drawing flowcharts.

Answer 1

The risk with using a factorial function is that it very quickly goes out of int range. There is no need to have either a power function or a factorial function, because each term of the Taylor series can be derived from the previous term, by using a multiplication and a division.

The multiplier is self-evident, simply the square of the angle.

The divisor is i * (i - 1), the next two terms of the factorial.

You will see I have removed your sign change factor t, because to change the sign of the previous term from neg to pos, or pos to neg, you just multiply by -1. But I have even removed that by reversing the sign of (i - 1) with my use of (1 - i).

The first term of the series is simply rad so I start with that.

#include <stdio.h>
#include <math.h>

int main()
{
    int n, i;                                       // don't use `l` for a variable name 
    float deg, rad, radsq, val, term;

    printf("Enter degree of sin: ");
    if(scanf("%f", &deg) != 1) {
        return 1;                                   // or other error handling
    }

    printf("Enter limit of Taylor series: ");  
    if(scanf("%d", &n) != 1) {                           
        return 1;                                   // or other error handling
    }
    rad = deg * 3.14159265f / 180;                  // proper value for pi
    radsq = rad * rad;

    term = rad;                                     // first term is rad
    val = term;                                     // so is series sum
    for(i = 3; i <= n; i += 2)                      // we've done the first term
    {
        term *= radsq / (i * (1 - i));              // see explanation
        val += term;                                // sum the series
    }

    printf("
Value calculated by program, using Taylor Series:
");
    printf("Sin(%f) = %f
", deg, val);
    printf("
Value calculated using library function:
");
    printf("Sin(%f) = %f
", deg, sin(rad));

    return 0;
}