4 replies to this topic

[rioters block]

hello everyone. In my CS class we're doing trying to compute some taylor series expansions of basic math functions and thereby learning a lot about doing infinite summations on the computer. My assignment was to compute the cosine of whatever value I choose for x.

cos(x) = 1 - (x^2)/2! + (x^4)/4! - (x^6)/6! + ......

Now, I've written two programs, both of which use while loops, however they have diffrent terminating conditions. And, for smaller values of x they both get the exact answer you would when you use the cosine function in <cmath>. However, if you choose x to be 100 or something, there's a huge discrepancy between my program's answer and cmath.

I'm worried that I might be initializing the values of term and the sums incorrectly. If I'm not, then I'm stumped as to what i'm doing wrong! Here's my code, and if you guys can maybe make a suggestion, it would be sweet!

#include<iostream>
#include<cmath>
using namespace std;

int main()
{
     double x, term = 1, oldsum = 0, newsum = term;
     int i = 1;
     cout<<"Enter value of x in radians:"<<endl;
     cin>>x;
     while(oldsum != newsum) 
*/the loop should stop when there's no more diffrence between the old and new sum (i.e the term has become too small to make a diffrence) */
     {
         oldsum = newsum;
         term = fabs(term)*pow(-1.0,i)*pow(x,2)/(2*i*(2*i-1));
         newsum += term;
         ++i;
     }
     cout<<"cos("<<x<<") = "<<newsum<<endl;
     cout<<"cos("<<x<<") = "<<cos(x)<<endl;
     system("pause");
     return 0;
}

Edited by Jaan, 21 September 2009 - 08:41 AM.

[WingedPanther]

The code you've implemented does correctly calculate the term. You aren't calculating the factorial at all, and the power is 2*i, not 2!

[rioters block]

WingedPanther said:

The code you've implemented does correctly calculate the term. You aren't calculating the factorial at all, and the power is 2*i, not 2!

I don't understand what you mean? Am I calculating the term wrong? I couldn't use the factorial function in cmath since it would get too large too quickly, that it would be bigger than INT_MAX which isn't good, so I had to go with this way. What did you mean that the power is 2*i?

[dargueta]

I think he meant:

pow(x,2)
//should be
pow(x,2*i)

[WingedPanther]

You have to use factorial. If you don't, you will get incorrect results (as you discovered)!