Calculating cosine using recursion problems

To expand on the title of the thread, I have been having trouble creating a proper cosine function that uses recursion. I don't want to use any form of a loop in this code. I have tried everything I can think of to accomplish this, but I haven't had any luck so far. Here is the code:

#ifndef M_PI
#define M_PI 3.141592653589793238462643383279502884197169399
#endif

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

long long factorial(long long num);
long double cosine(long double angle);
double constrainAngle(double x);
char safeChoice(string prompt, char choice1, char choice2);

const double CUT_OFF = 0.0001;
const int BUFFER_SIZE = 256;

int main(void)
{
	long double angle = 0.0;
	long double radAngle = 0.0;
	long double c = 0.0;
	char ch;
	string deg = " ";
	
	cout << "Input an angle in radians: ";
	cin >> angle;

	if (!cin.fail())
	{
		deg = angle == 1 ? " degree" : " degrees";
		cout << "The cosine() approximation at " << angle
			<< deg << " is equal to: " << setprecision(3)
			<< cosine(angle) << endl;
		cout << setprecision(3)
			<< "The cos() function in the cmath library for this angle returns: "
			<< cos(angle) << endl;
		cin.get();
		cout << endl;
		cin.get();
		ch = safeChoice("Calculate another cosine?", 'Y', 'N');
		cout << endl;
		if (tolower(ch) == 'n')
		{
			return EXIT_SUCCESS;
		}
		else
		{
			main();
		}
	}
	else
	{
		cin.clear();
		cout << "That is not a number. Press enter." << endl;
		cin.get();
		cin.get();
		main();
	}
}

long long factorial(long long num)
{
	if(num < 0LL)
		throw exception();
	long long temp;
	
	if(num <= 1LL)
		return 1LL;
	temp = num * factorial(num - 1);
	return temp;
}

long double cosine(long double angle)
{  
	static int n = 0;
	static long double sum = 0.0;
		
	if(fabs(n) >= CUT_OFF)
	{
		n++;
		sum += (pow(angle, n * 2) / factorial(2 * n));
		cosine(angle);
	}
	else
	{
		return sum;
	}
}

double constrainAngle(double x)
{
	x = fmod(x, 2 * M_PI);
	if (x < 0)
		x += (2 * M_PI);
	return x;
}

The safeChoice() function is not necessary to understand my problem, so I haven't included it in the code I put here.

I also need to figure out how to not make main() recursive, as someone told me that just uses up memory every time the user enters a letter to fit that condition.

I have searched Google for about a week now to find an answer; still no luck from that. I basically need to understand why the code I have isn't working, and to understand how to fix it.