Question

I’m writing a sine function that has to be recursive. I have written a sine function but am not really sure how to do it recursively. Could someone explain how to get started on this?

This is what I have so far:

/*--------------------------------------------------------------
Name: sine( double X );

Return: Function "sine" will return the 
sine of X, where X is measured in radians.
--------------------------------------------------------------*/

double sine(double X)
{
  double result = 0;
  double term;
  int k;
  double lim;

  k = 0;
  lim = power(10, -8); 
  term = power(-1, k)*power(X, ((2*k) + 1)) / (factorial((2*k)+1));  
  result = term;
  while (absolute(term) > lim)  
  {
    k += 1;
    term = power(-1, k)*power(X, ((2*k) + 1)) / (factorial((2*k)+1));  
    result += term;
  }


  return result;
}

EDIT: I used a wrapper function to solve this. Basically created another function called

double sine_rec(double X, double k)

and changed around the current code to fit in with that.

Answer 1

The way I would approach this would be to have another function sine(double X, int n) which takes another integer parameter – the number of terms to include in the power series approximation. Then this function could return something like [nth term in series] + sine(X, n - 1) (just remember a prior if statement to deal with n = 1).