How do I find the derivative of sin(x) using recursion?

How do I find the derivative of sin(x) where x c开发者_JAVA百科ould be any value e.g. 1,2,3 using recursion?

Firstly, the derivative of sin(x) is cos(x) or, to put it more formally:

f(x) = sin(x)
f'(x) = cos(x)

I guess you could solve sin(x) using the Taylor series for cos(x):

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

with recursion. In Java:

public double cos(double x) {
  return 1 + next(-x*x/2, x, 3);
}

public double next(double term, double x, int i) {
  double next = -term * x * x / (i * (i + 1));
  return term + next(term, x, i + 2);
}

Of course you'll need to put some limiter in to exit the recursion otherwise you'll get a stack overflow error eventually, which is left as an exercise for the reader.

Oh and I see the question is tagged as C not Java, but it is homework. :-)