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

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

C++

// 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; 
} 

Java

// 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. 

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#

// 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. 

PHP

<?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 
?> 

Output :

0.642701

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

C

// 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); 
} 

Java

// 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 

Python3

# 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 

C#

// 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 

PHP

<?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 
?> 

Output :

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

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My Personal Notes

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

C++

Java

Python3

C#

PHP

C

Java

Python3

C#

PHP

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