CODEWITHSUNDEEP
ctrigonometrytaylor-series
Jordi García
Jordi García

Reputation: 43

Trying to generate the value of cos x using taylor's formula

The user is meant to give the value of "x" and "n" in order to calculate cos x using taylors series approximation ( you can check out its formula here: http://campusdematematicas.com/wp-content/uploads/2012/05/serie-taylor-funcion-coseno.gif) where the "k" value is the "i" in the code below.

The thing is that i dont know what i have done wrong, because it doesn't give me the proper value of cos x.

The input i just tried was x=3.14, and n=6. And the result it was supposed to give me was cosx = -1.00 Instead, it gave me: 1.14

By the way, it does not work for 0, as it should give cos (x) = 1.00, and it gives 0.000000 instead

#include <stdio.h>

int main(){
double x, n, m;
int i = 0, j, l, k = -1;
double g = 0.0;
unsigned long long p = 1;
printf("Introduce the value of x (real): ");
scanf("%lf%*c", &x);
m = x;
printf("\nIIntroduce the value of n (natural): ");
scanf("%lf%*c", &n);

while (i <=n){

    for (l=1; l < (i*2); l++){
    m *= x; 
    }

    for (j=1; j <= (2*i); j++){
        p *=j;

    }
    if (i%2 == 0){  
        k = 1;
    }

    g += (double) (m/p)*(k);
    p = 1;
    k = -1;     
    m = x;
    i++;
}
printf("\ncos(%.2lf) = %lf\n", x, g);
}

Upvotes: 2

Views: 389

Answers (1)

chux
chux

Reputation: 153303

Wrong initialization for m. Code is summing odd powers of x, rather than the even ones.

// m = x;
m = 1.0;

Output

cos(0.00) = 1.000000
cos(1.05) = 0.500460   // cos(60 degrees) --> 0.5
cos(1.57) = 0.000796   // cos(90 degrees) --> 0.0
cos(3.14) = -0.999899

Upvotes: 1

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