计算0~359度的余弦值，计算平均需要计算得到结果的最后一个n的大小，n从0开始。随着n的增大，每一项也是非常昂贵的计算。

这是第一种计算方法，把范围缩小到0到90度，fac的返回值可以不用longlong，平均需要计算n到5.13889，

#pragma warning(disable:4996)
#include<stdio.h>  
#include<string.h>  
#include<iostream>
#include<functional>
#include<queue>
#include<set>
#include<string>
#include<unordered_map>
#include<map>
#include<array>
#include<algorithm>
#include<stack>
using namespace std;
#define PRECISION 1e-5
#define PI acos(-1.0)
int cnt = 0;
int fac(int index)
{
	int ans = 1;
	while(index)
	{
		ans *= index;
		--index;
	}
	return ans;
}
double _cos(int angle)
{
	angle %= 360;
	while (angle < 0) angle += 360;
	bool reverse = false;
	if(angle >= 180)
	{
		angle -= 180;
		reverse = true;
	}
	if(angle > 90)
	{
		reverse = !reverse;
		angle = 180 - angle;
	}
	double x = PI * angle / 180;
	while(x < 0)	x += PI;
	while (x > 2 * PI) x -= 2 * PI;
	int index = 0;
	double ans = 0, delta = 1;
	while (abs(delta) > PRECISION)
	{
		delta = pow(-1, index)*pow(x, index * 2) / fac(2 * index);
		++index;
		ans += delta;
		cnt++;
	}
	return reverse ? -ans : ans;
}
int main()
{
	int angle = 0;
	for(int i = 0; i < 360; ++i)
	{
		_cos(i);
	}
	cout << cnt * 1.0 / 360 << endl;
	system("pause");
}

这是第二种计算方法，把范围缩小到0到180度，使用longlong，因为直接计算到360度还是会爆longlong，所以缩小到180度，平均计算的n的值为6.55556

#pragma warning(disable:4996)
#include<stdio.h>  
#include<string.h>  
#include<iostream>
#include<functional>
#include<queue>
#include<set>
#include<string>
#include<unordered_map>
#include<map>
#include<array>
#include<algorithm>
#include<stack>
using namespace std;
#define PRECISION 1e-5
#define PI acos(-1.0)
long long cnt = 0;
long long fac(int index)
{
	long long ans = 1;
	while(index)
	{
		ans *= index;
		--index;
	}
	return ans;
}
double _cos(int angle)
{
	angle %= 360;
	while (angle < 0) angle += 360;
	bool reverse = false;
	if(angle >= 180)
	{
		angle -= 180;
		reverse = true;
	}
	double x = PI * angle / 180;
	while(x < 0)	x += PI;
	while (x > 2 * PI) x -= 2 * PI;
	int index = 0;
	double ans = 0, delta = 1;
	while (abs(delta) > PRECISION)
	{
		delta = pow(-1, index)*pow(x, index * 2) / fac(2 * index);
		++index;
		ans += delta;
		cnt++;
	}
	return reverse ? -ans : ans;
}
int main()
{
	int angle = 0;

	for (int index = 0; index < 360; ++index)
	{
		cout << _cos(index) << " " << index << endl;
			
	}
	cout << cnt * 1.0 / 360 << endl;
	system("pause");
}