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++

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// 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;
}

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Java

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// 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.

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Python3

# 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

C#

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// 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.

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PHP

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<?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
?>

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Output :

0.642701

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

C

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// 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);
}

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Java

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// 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

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Python3

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# 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

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C#

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// 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

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PHP

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<?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
?>

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Output :

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


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