CODEWITHSUNDEEP
c
reallybadprogrammer
reallybadprogrammer

Reputation: 27

Summation of terms not returning correct result

I have this academic project in C language. One of the exercises is calculating cos(x) without using math.h. For that, we're given a series (which I presume it's a Taylor/Maclaurin) for cos(x). For standard input, we have x angles, and k iterations. The sum is from n=0 to k-1 of ((-1)^n*x^(2n))/(2n)!

I've tried changing in and out of cycles and fiddling with variables with no avail.

Here is the code (UPDATED):

#include <stdio.h>

int fat(int num) {
    int fat_num=1;
    for (int cnt=1; cnt<=num; cnt++) fat_num*=cnt;
    return fat_num;
}

float expn(int x, int y) {
    int x_y=x;
    for (int cnt=1; cnt<y; cnt++) x_y*=x;
    return x_y;
}

int main() {
    const float pi = 3.1415926;
    float x; 
    scanf("%f",&x);
    int k; 
    scanf("%d", &k);
    float cosx = 0;
    int n = 0;
    x *= pi/180;
    while (n <= k-1) {
        if (n%2 == 0) 
            cosx +=    expn(x,2*n)/fat(2*n);
        else 
            cosx += -1*expn(x,2*n)/fat(2*n);
        n++;
    }
    printf("%f", cosx);
    return 0; 
}

The input of 96 gives me a cossine of 0.54. Which is not right.

Solved: The error was in expn which had to be updated to float!

Upvotes: 0

Views: 79

Answers (1)

chux
chux

Reputation: 154087

2 problems

expn(x,2*n)/fat(2*n) uses integer division.

float expn(int x, int y) uses an int x. Need floating point x.

// int expn(int x, int y) {
float expn(float x, int y) {
  float x_y = 1;
  for (int cnt = 0; cnt < y; cnt++)
    x_y *= x;
  return x_y;
}

Code has various efficiencies.

An alternative that does not need k - some food for thought.

static double my_cos_helper(double xx, double term, unsigned n) {
  if (term + 1.0 == 1.0) {
    return term;
  }
  return term - xx * my_cos_helper(xx, term / ((n + 1) * (n + 2)), n + 2);
}

double my_cos(double x) {
  return my_cos_helper(x * x, 1.0, 0);
}

Upvotes: 1

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