用于计算正弦的C程序给出了不准确的结果

Question

I have to write this program only with #include<stdio.h> .

I have to read the highest power of the series 'n' from the user.

When x=45 and n=9 , then the program gives me 0.7068251967 . But when I use my calculator for the same then I get 0.7068251828 .

I also have to use recursion.

#include<stdio.h>

float pow(float n, int p)
{
if(p == 0)
    return 1;
else
    return n * pow(n, p-1);
}

int fact(int n)
{
if(n == 0)
    return 1;
else
    return n * fact(n-1);
}

int main()
{
int n, x, i, sign = 1;
float sum, r;


printf("Enter the angle in degrees.\n");
scanf("%d", &x);

r = 3.14 * x / 180.0;

printf("Enter the odd number till which you want the series.\n");
scanf("%d", &n);

if(n % 2 == 0)
    printf("The number needs to be an odd number.\n");
else
{


for(i = 1, sum = 0; i <= n; i += 2, sign *= -1)
{
    sum += (sign * pow(r, i)) /  fact(i);
}

printf("The sum of the series is %.10f.\n", sum);
}


return 0;
}

Answer 1

I think one cause is the fact that you approximate pi by 3.14. Maybe your calculator takes into consideration more digits of pi. Try using more digits for approximatig pi.

Answer 2

@Mat is right, use M_PI instead of your 'poor man' 3.14. Besides do not always exponentiate x to the power n or factorials. Notice that the next term of the sum: a_{k+2}=-a_{k}x^2/(k(k-1)), (the even terms are zero) Use something like

double s=x,a=x,x2=-x*x;
int i;
for (i=3;i<=n;i+=2)
{
   a*=x2/i/(i-1);
   s+=a;
}