求用C++语言编写y=sinx,用泰勒公式

Question

这是我的

#include <iostream>
# include <cmath>
using namespace std;
double potenz(double n,unsigned int x);
double fakult(unsigned int n);
double iteration(double x);
double ungerade(unsigned int n);
void eingabe(double &x);
——————————————————————————————————
#include "Deklaration.h"
double potenz(double x,unsigned int n)
{
double pot=1;
for(unsigned int i=1;i<=n;i=i++)
pot=pot*x*x;
return pot;
}
double fakult(unsigned int n)
{
double fak=1;
for(unsigned int i=1;i<=2*n+1;i=i+1)
fak=fak*i;
return fak;
}
double ungerade(unsigned int n)
{
double ung=1;
for(unsigned int i=1;i<=n;i=i+2)
ung=-1*ung;
return ung;
}
double iteration(double x)
{
double s=0;
unsigned int i=0;
while (fabs(potenz(x,i)/fakult(i))>1e-8)
{
s=s+potenz(x,i)/fakult(i)*ungerade(i);
i=i+1;
}
return s;
}
void eingabe(double &x)
{ cout<<"x=";
cin>>x;
}
——————————————————————————————————
#include "Deklaration.h"
int main ()
{

double z;
cout<<"Berechnung von f(x)=sin(x)"<<endl;
eingabe(z);
cout<<"sin(x)="<<iteration(z)<<endl;
cout<<"sin(x)="<<sin(z)<<endl;
return 0;
}

呃~德语单词请无视= =

谢谢啦~

Answer 1

貌似你的写得很复杂……我最近自己写了个，比较简单，可以参考一下

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

int main()
{
double x;
double sinx;
int a = 1; //控制正负相间
double b; //记录x的分母次方
double c = 1.0; //分母
double d = 1.0; //记录分母的阶乘
double temp; //记录泰勒公式每项的值
cin>>x;
sinx = x; //第一项
b = x; //b的初始化
do
{
a = -a; //正负变换
c += 2; //分母加2规律
d *= c*(c-1); //分母阶乘累积
b *= x*x; //分子乘积累积
temp = a*b/d; //计算泰勒公式的某一项
sinx += temp; //把这项加到总和
}while(fabs(temp) > 0.000001); //如果某一项的值还大于这个精度
cout<<sinx<<endl;
return 0;
}

Answer 2

// 原函数 return x 的n次方
// 改成
// return x的2n+1次方
double potenz(double x,unsigned int n)
{
double pot=1.0;
for(unsigned int i=1;i<=(2*n+1);i++)
pot *=x;
return pot;
}

// 阶乘 (2n+1)!
double fakult(unsigned int n)
{
double fak=1.0;
for(unsigned int i=1;i <= (2*n+1);i++)
fak *= i;
return fak;
}

// 决定某项的符号
// 偶数项为正
// sin(x) = x - x^3/3! + x^5/5! ...
// 其中x单独计算，所以序列为
// -x^3/3! + x^5/5! ...
double ungerade(unsigned int n)
{
if(n%2)
return (-1.0);
return (1.0);
}
//求各项和
double iteration(double x)
{
//第一项
double s(x);
unsigned int i=1;
while (fabs(potenz(x,i)/fakult(i))>1e-8)
{
s += (potenz(x,i) * ungerade(i) / fakult(i) );
i++;
}
return s;
}