CODEWITHSUNDEEP
c
Avishay28
Avishay28

Reputation: 2456

Calculate cosine with sum of addends

Need some help with a task from my homework. They gave us a series to calculate cosine, which is: Σ(-1)^ix^2i/(2i)! And the task is to implement this in C program by writing a function that takes angle x, and calculate it's cosine. The series should continue summing until the next addend in the series is less then 1.0e-6 (0.000001). I did this and it works good only for small numbers, if I put big numbers as angle, the program get stuck.

#include <stdio.h>
#include <math.h>
#define PI 3.141592

double my_cos(double angle);

int main() {
    double angle, radian,  my_res, their_res;

    printf("Please type a number... \n");
    scanf("%lf", &angle);

    radian = angle * (PI/180);


    my_res = my_cos(radian); /* result from my custom cosine function */
    their_res = cos(radian); /* result from the cos function located in the library math.h */

    printf("My result is: %f \nMath.h library result is: %f \n", my_res, their_res);

    return 0;
}

.

#include <math.h>
#define ACCURACY 1.0e-6

long factorial(int x);


double my_cos(double angle){
    int i = 0;
    double sum = 0,  next_addend;

    do {
        next_addend = pow(-1, (i+1)) * pow(angle, 2*(i+1)) / factorial(2*(i+1));
        sum += pow(-1, i) * pow(angle, 2*i) / factorial(2*i);

        i++;
    } while ( ACCURACY < fabs(next_addend) );

    return sum;
}

/* return the factorial of a given value */
long factorial(int x){
    if ( x == 0 ) {
        return 1;
    }

    return(x * factorial(x - 1));
}

If I run the program and insert 45: enter image description here

But if I insert 300, the program is just "waiting": enter image description here

I guess it related somehow to the factorial function? I will really appreciate your help..

Upvotes: 0

Views: 135

Answers (1)

chtz
chtz

Reputation: 18807

Depending on whether sizeof(long) is 4 or 8 on your system you can only calculate 12! or 20! inside a long. Also, calculating multiple pow at every iteration is very inefficient.

For a better solution, try to find out how to calculate the next_addend if you know the previous addend (hint: calculate their ratio on a piece of paper).

Upvotes: 4

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