help calculating sine using factorials equation

darkangel29 · 09-28-2007, 07:24 PM

I write this code that all it does is calculate sine using the formula sin(x) = x − x^3/3! + x^5/5! - x^7/7! + x^9/9!...
Problem is when I look for the sine of 90 it tells me is 0.999408 instead of just one. How can I fix this??

Code:

#include <cstdlib>
#include <iostream>
#include <cmath>
#define PI 3.14159265358979323846
using namespace std;
int factorial(int);
void Sin(double &x,int n);

int main()
{
double angle=0;
double x=0;
cout<<"Input an angle and I will compute the sine of that angle:\n";
cin>>angle;

x=angle*(PI/180);

cout<<"sin("<<x<<") = ";
Sin(x,15);

return 0;
}
int factorial(int n)
{
if(n==0||n==1){
return 1;
}
else
return (n*factorial(n-1));
}
void Sin(double &x,int n)
{
double temp=0;
for(int i=0;i<n;i++){
temp+=(pow((double)(-1),(double)(i))*pow((double)(x),(double)(2*i+1)))/(double)(factorial(2*i+1));
}
cout<<temp<<endl;
}

choogendyk · 09-28-2007, 09:56 PM

Have you played with that n, which is 15 in Sin(x,15)?

What happens if you change it lower and higher? You could make a table of n vs estimate of Sin(x,n). Watch how it converges.

Aside from that, you're going to be getting deeper into computational and numerical methods, the cumulative effect of roundoff error, etc. You could take a course in that. Somewhere up in my attic I have a huge thick hardback book on Numerical Methods in Fortran. You could dig up something like that for C.

Dan04 · 09-28-2007, 10:39 PM

This one gives sin(90°) = 1.0000000000000002:

Code:

double Sin(double x, int n)
{
   int    i;
   double term = x;
   double result = x;

   for (i = 3; i <= n; i += 2)
   {
      term *= -(x * x) / ((i - 1) * i);
      result += term;
   }

   return (result);
}

darkangel29 · 09-29-2007, 12:20 PM

Thanks a lot!!! Appreciate the help.
Now all I want to know is how do I round off numbers like 0.4999 to just 0.50?? I believe this can be done with the float command. Can somebody point me to the right direction? Thanks.

This is my new code

Code:

#include <cstdlib>
#include <iostream>
#include <cmath>
#define PI 3.141
using namespace std;
int factorial(int);
double Sin(double x,int n);

int main()
{
double angle=0;
double x=0, res_sin;
cout<<"Input an angle and I will compute the sine of that angle:\n";
cin>>angle;

x=angle*(PI/180);

cout<<"sin("<<x<<") = ";
res_sin=Sin(x,15);
cout<<res_sin<<endl;

return 0;
}
int factorial(int n)
{
if(n==0||n==1){
return 1;
}
else
return (n*factorial(n-1));
}
double Sin(double x, int n)
{
   int    i;
   double term = x;
   double result = x;

   for (i = 3; i <= n; i += 2)
   {
      term *= -(x * x) / ((i - 1) * i);
      result += term;
   }

   return (result);
}