c++紧急，十万火急

#include <iostream>
#include <cmath>
using namespace std;
double sin(double x);
double fac(int i);
double pow(double x,int i);
int main()
{
double m;
m=0.1*sin(0.1)+sin(0.2)+sin(0.3)+sin(0.4)+sin(0.5)+sin(0.6+sin(0.7)+sin(0.8)+sin(0.9)+sin(1));
cout<<"∫sinxdx在区间[0,1]上的值为"<<m<<endl;
return 0;
}
double sin(double x)
{ double y=0;
double t;
double k;
int i=1,a=1;
{t=a*pow(k,i)/fac(i);
y=y+t;
i=i+2;
a=-a;}
return y;
}
double pow(double x, int i)
{if (i==1)
return x;
return pow(x,i-1)*x;
}

double fac(int i)
{double fac(int i);
int f=1,b=1;
while (b<=i)
{ f=f*b;b++;}
return f;
}

编译时系统总是提示k没有初始化。为什么？要怎样改才能使其正常运行并能得出正确结果？
给个调用sinx函数的程序

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