Question

Problem1. Write a C program, called cos.approx.c, that computes the approximate value of cos(x) according to its Tavlor series expansion: (-1)"r2n (2n)! x2 x4x6x8x10 cos(x)-Σ 1 This series produces the exact value of cos(x) for any real number x, but contains an infinite number of terms. Obviously, a computer program can compute only a finite number of terms. Thus, you will have to truncate the infinite series in (1). Your program should be able to do so in two different ways. Fixed number of terms: Implement the function cosוב ( double x, int N) that accepts as pa- rameters a real number x and an integer N (you can assume that N will be always positive). The function cos N should return the sum of the first N terms in (1), as a double. Fixed precision: Implement the function cos_delta (double x, double delta) that ac- cepts as parameters a real number x and another real number δ (you can assume that δ will be always positive). The function cos delta should return, as a double, the sum of the first NN terms in (1), where N is the smallest positive integer such that

Answer 1

Here's the program written as per the given specifications. Please do rate the answer if you found this helpful.

Code:

#include <stdio.h>

int factorial(int n)

{

if(n == 0) return 1;

else return n * factorial(n-1);

}

double power(double x, int n)

{

if(n == 0) return 1;

else if(n%2 == 0) return power(x, n/2) * power(x, n/2);

else return x * power(x, n/2) * power(x, n/2);

}

double cos_n(double x, int n)

{

double approx = 0;

// // for n times.

for(int i=0; i<n; i++)

{

approx += power(-1, i) * power(x, 2*i)/factorial(2*i);

}

return approx;

}

double cos_delta(double x, double delta)

{

double approx = 0, last_approx = 0, current_term = 0;

// variable for maintaing absolute difference between last_approx and approx.

double absDiff = 0;

int i=0;

do

{

last_approx = approx; // update last approx.

current_term = power(-1, i) * power(x, 2*i)/factorial(2*i); // calculate current term.

approx += current_term; // update current aprrox.

i++;

absDiff = (last_approx-approx > 0) ? last_approx-approx : approx-last_approx; // find the abs difference.

}while(absDiff > delta); // loop till difference is greater than delta.

return approx;

}

int main(void)

{

FILE *inFile = fopen("cos_input.dat", "r");

FILE *outFile = fopen("cos_output.dat", "w");

if(!inFile || !outFile)

{

printf("Error opening files!");

return 1;

}

int testcases = 0;

fscanf(inFile, "%d", &testcases);

int functionType = 1;

double x;

double delta;

int numTerms;

double cosApprox = 0;

for(int i=0;i <testcases; i++)

{

fscanf(inFile, "%d", &functionType);

if(functionType == 1)

{

fscanf(inFile, "%lf %d", &x, &numTerms);

cosApprox = cos_n(x, numTerms);

}

else

{

fscanf(inFile, "%lf %lf", &x, &delta);

cosApprox = cos_delta(x, delta);

}

// writing to file the output.

fprintf(outFile, "\nCase %d: cos(%.3lf) = %.12lf", (i+1), x, cosApprox);

}

return 0;

}

Sample Input file:

Sample output file: