Program for sum of cos(x) series

Given n and b, where n is the number of terms in the series and b is the value of the angle in degree.
Program to calculate the sum of cosine series of x and compare the value with the library function’s output.

Formula Used :

cos x = 1 – (x2 / 2 !) + (x4 / 4 !) – (x6 / 6 !) +…

Examples :

Input : n = 3
        x = 90
Output : Sum of the cosine series is =  -0.23
The value using library function is = -0.000204

Input : n = 4
        x = 45
Output : 
Sum of the cosine series is = 0.71
The value using library function is = 0.707035

C++

filter_none

edit
close

play_arrow

link
brightness_4
code

// CPP program to find the 
// sum of cos(x) series
#include <bits/stdc++.h>
using namespace std;
  
const double PI = 3.142;
  
double cosXSertiesSum(double x, 
                      int n)
{
    x = x * (PI / 180.0); 
  
    double res = 1;
    double sign = 1, fact = 1, 
                     pow = 1;
    for (int i = 1; i < 5; i++)
    {
        sign = sign * -1;
        fact = fact * (2 * i - 1) * 
                           (2 * i);
        pow = pow * x * x;
        res = res + sign * 
              pow / fact;
    }
  
    return res; 
}
  
// Driver Code
int main() 
{
    float x = 50;
    int n = 5;
    cout << cosXSertiesSum(x, 5);
    return 0;
}

chevron_right


Java

filter_none

edit
close

play_arrow

link
brightness_4
code

// Java program to find
// the sum of cos(x) series
import java.lang.Math.*;
  
class GFG 
{
    static final double PI = 3.142;
      
    static double cosXSertiesSum(double x, 
                                 int n)
    {
        x = x * (PI / 180.0); 
      
        double res = 1;
        double sign = 1, fact = 1
                         pow = 1;
        for (int i = 1; i < 5; i++)
        {
            sign = sign * -1;
            fact = fact * (2 * i - 1) * 
                               (2 * i);
            pow = pow * x * x;
            res = res + sign * pow / fact;
        }
      
        return res; 
    }
      
    // Driver Code
    public static void main(String[] args) 
    {
        float x = 50;
        int n = 5;
        System.out.println((float)(
            cosXSertiesSum(x, 5) * 1000000) / 
                                 1000000.00);
    }
}
  
// This code is contributed by Smitha.

chevron_right


Python3

filter_none

edit
close

play_arrow

link
brightness_4
code

# Python3 program to find the 
# sum of cos(x) series
  
PI = 3.142;
  
def cosXSertiesSum(x, n):
      
    x = x * (PI / 180.0); 
  
    res = 1;
    sign = 1
    fact = 1;
    pow = 1;
    for i in range(1,5):
        sign = sign * -1;
        fact = fact * (2 * i - 1) * (2 * i);
        pow = pow * x * x;
        res = res + sign * pow / fact;
  
    return res; 
  
# Driver Code
x = 50;
n = 5;
print(round(cosXSertiesSum(x, 5), 6));
  
# This code is contributed by mits

chevron_right


C#

filter_none

edit
close

play_arrow

link
brightness_4
code

// C# program to find the
// sum of cos(x) series
using System;
  
class GFG 
{
    static double PI = 3.142;
      
    static double cosXSertiesSum(double x, 
                                 int n)
    {
        x = x * (PI / 180.0); 
      
        double res = 1;
        double sign = 1, fact = 1, 
                         pow = 1;
        for (int i = 1; i < 5; i++)
        {
            sign = sign * -1;
            fact = fact * (2 * i - 1) * 
                               (2 * i);
            pow = pow * x * x;
            res = res + sign * pow / fact;
        }
      
        return res; 
    }
      
    // Driver Code
    public static void Main() 
    {
        float x = 50;
        int n = 5;
        Console.Write((float)(cosXSertiesSum(x, n) * 
                             1000000) / 1000000.00);
    }
}
  
// This code is contributed by Smitha.

chevron_right


PHP

filter_none

edit
close

play_arrow

link
brightness_4
code

<?php
// PHP program to find the 
// sum of cos(x) series
  
$PI = 3.142;
  
function cosXSertiesSum($x, $n)
{
    global $PI;
    $x = $x * ($PI / 180.0); 
  
    $res = 1;
    $sign = 1; $fact = 1; 
               $pow = 1;
    for ( $i = 1; $i < 5; $i++)
    {
        $sign = $sign * -1;
        $fact = $fact * (2 * $i - 1) * 
                             (2 * $i);
        $pow = $pow * $x * $x;
        $res = $res + $sign * $pow
                              $fact;
    }
  
    return $res
}
  
// Driver Code
$x = 50;
$n = 5;
echo cosXSertiesSum($x, 5);
  
// This code is contributed by aj_36
?>

chevron_right


Output :



0.642701

Note that we can also find cos(x) using library function.

C++

filter_none

edit
close

play_arrow

link
brightness_4
code

// C++ code to illustrate
// the use of cos function
#include <bits/stdc++.h>
using namespace std;
  
#define PI 3.14159265
  
int main ()
{
    double x, ret, val;
      
    x = 60.0;
    val = PI / 180.0;
    ret = cos(x * val);
    cout << "The cosine of " << fixed 
         << setprecision(6) << x << " is ";
    cout << fixed << setprecision(6)
         << ret << " degrees" << endl;
           
    x = 90.0;
    val = PI / 180.0;
    ret = cos(x * val);
    cout << "The cosine of " << fixed 
         << setprecision(6) << x << " is ";
    cout << fixed << setprecision(6) 
         << ret << " degrees" << endl;
      
    return(0);
}
  
// This code is contributed by shubhamsingh10

chevron_right


C

filter_none

edit
close

play_arrow

link
brightness_4
code

// C code to illustrate
// the use of cos function
#include <stdio.h>
#include <math.h>
  
#define PI 3.14159265
  
int main ()
{
double x, ret, val;
  
x = 60.0;
val = PI / 180.0;
ret = cos( x * val );
printf("The cosine of %lf is ", x);
printf("%lf degrees\n", ret);
      
x = 90.0;
val = PI / 180.0;
ret = cos( x*val );
printf("The cosine of %lf is ", x);
printf("%lf degrees\n", ret);
      
return(0);
}

chevron_right


Java

filter_none

edit
close

play_arrow

link
brightness_4
code

// Java code to illustrate
// the use of cos function
import java.io.*;
  
class GFG 
{
static final double PI = 3.142;
public static void main (String[] args)
{
    double x, ret, val;
      
    x = 60.0;
    val =(int)PI / 180.0;
    ret = Math.cos(x * val);
    System.out.print("The cosine of "
                           x + " is ");
    System.out.print(ret);
    System.out.println(" degrees");
          
    x = 90.0;
    val = (int)PI / 180.0;
    ret = Math.cos( x*val );
    System.out.print("The cosine of " +
                           x + " is ");
    System.out.print(ret);
    System.out.println(" degrees");
}
}
  
// This code is contributed 
// by ajit

chevron_right


Python3

filter_none

edit
close

play_arrow

link
brightness_4
code

# Python3 code to illustrate
# the use of cos function
import math
  
if __name__=='__main__':
    PI = 3.14159265
  
    x = 60.0
    val = PI / 180.0
    ret = math.cos(x * val)
    print("The cosine of is ", x, end=" ")
    print(" degrees", ret)
  
    x = 90.0
    val = PI / 180.0
    ret = math.cos(x * val)
    print("The cosine of is ", x, end=" ")
    print("degrees", ret)
  
# This code is contributed by
# Sanjit_Prasad

chevron_right


C#

filter_none

edit
close

play_arrow

link
brightness_4
code

// C# code to illustrate
// the use of cos function
using System;
  
class GFG
{
      
// Constant PI Declaration 
static double PI = 3.142;
  
// Driver Code
static public void Main ()
{
    double x, ret, val;
      
    x = 60.0;
    val = (int)PI / 180.0;
    ret = Math.Cos(x * val);
    Console.Write("The cosine of "
                        x + " is ");
    Console.Write(ret);
    Console.WriteLine(" degrees");
          
    x = 90.0;
    val = (int)PI / 180.0;
    ret = Math.Cos(x * val);
    Console.Write("The cosine of " +
                        x + " is ");
    Console.Write(ret);
    Console.WriteLine(" degrees");
}
}
  
// This code is contributed 
// by akt_mit

chevron_right


PHP

filter_none

edit
close

play_arrow

link
brightness_4
code

<?php
//PHP code to illustrate
// the use of cos function
  
$PI =3.14159265;
  
$x; $ret; $val;
  
$x = 60.0;
$val = $PI / 180.0;
$ret = cos( $x * $val );
echo "The cosine of is ", $x;
echo "degrees", $ret;
echo "\n";
  
$x = 90.0;
$val = $PI / 180.0;
$ret = cos( $x * $val );
echo "The cosine of is ", $x;
echo "degrees ", $ret;
      
// This code is contributed by aj_36
?>

chevron_right


Output :

The cosine of 60.000000 is 0.500000 degrees
The cosine of 90.000000 is 0.000000 degrees

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.




My Personal Notes arrow_drop_up

Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.