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ctaylor-series

Approximating sin(x) using Taylor series until absolute value of a term goes below a certain real value

I want to print the value of sin(x) using its Taylor series.

I must add terms until the absolute value of a term becomes < 10e-06

#include <stdio.h>
#include <math.h>
double val(double, double);
int main(void){

    double x,eps=10e-06;

    printf("\nEnter value of x: ");
    scanf("%lf",&x);

    printf("\nCalculated value: %lf\n",val(x, eps));

    return 0;

}

double val(double x, double eps){

    int i;
    double t=x, sum=0;
    if(fabs(x)<= eps) return 0;

    for(i=1;i<=20; i++){

        sum+=t;
        t*=-(x*x)/((2*i+1)*(2*i));
        if(fabs(t)>=eps) break;
    }
    return sum;
}

But I am getting the same output as my input(that is I am getting x in output).

Can someone tell me what is wrong.

Solution

  • The problem is here:

    if(fabs(t)>=eps) break;

    You're breaking out of the loop if the term is greater than the epsilon value. You want to check if it's less:

    if(fabs(t)<eps) break;