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Program for sum of cos(x) series

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  • Difficulty Level : Medium
  • Last Updated : 17 Oct, 2022
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Given n and x, where n is the number of terms in the series and x is the value of the angle in degree. 
Program to calculate the value of cosine of x using series expansion formula 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++




// CPP program to find the
// sum of cos(x) series
#include <bits/stdc++.h>
using namespace std;
 
const double PI = 3.142;
 
double cosXSeriesSum(double x, int n)
{
    // here x is in degree.
    // we have to convert it to radian
    // for using it with series formula,
    // as in series expansion angle is in radian
 
    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 << cosXSeriesSum(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 cosXSeriesSum(double x,
                                 int n)
    {
          // here x is in degree.
        // we have to convert it to radian
        // for using it with series formula,
        // as in series expansion angle is in radian
       
        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)(
            cosXSeriesSum(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 cosXSeriesSum(x, n):
     
    # here x is in degree.
    # we have to convert it to radian
    # for using it with series formula,
    # as in series expansion angle is in radian
     
    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(cosXSeriesSum(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 cosXSeriesSum(double x,
                                 int n)
    {
          // here x is in degree.
        // we have to convert it to radian
        // for using it with series formula,
        // as in series expansion angle is in radian
         
          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)(cosXSeriesSum(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 cosXSeriesSum($x, $n)
{
    global $PI;
   
   
    // here x is in degree.
    // we have to convert it to radian
    // for using it with series formula,
    // as in series expansion angle is in radian
   
    $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;
$n = 5;
echo cosXSeriesSum($x, 5);
 
// This code is contributed by aj_36
?>


Javascript




<script>
 
// Javascript program to find
// the sum of cos(x) series
 
const  PI = 3.142;
 
    function cosXSeriesSum( x, n) {
        // here x is in degree.
        // we have to convert it to radian
        // for using it with series formula,
        // as in series expansion angle is in radian
 
        x = x * (PI / 180.0);
 
        let res = 1;
        let sign = 1, fact = 1, pow = 1,i;
        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
      
        let x = 50;
        let n = 5;
        document.write( ((cosXSeriesSum(x, 5) * 1000000) / 1000000.00).toFixed(6));
 
// This code is contributed by shikhasingrajput
 
</script>


Output : 

0.642701

 

Time complexity: O(1)
Auxiliary space: O(1)

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

C++




// 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


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
?>


Javascript




<script>
 
// javascript code to illustrate
// the use of cos function
    var PI = 3.142;
 
    var x, ret, val;
     
    x = 60.0;
    val = PI / 180.0;
    ret = Math.cos(x * val);
    document.write("The cosine of " +
                           x + " is ");
    document.write(ret.toFixed(5));
    document.write(" degrees");
    document.write("<br>"
     
    x = 90.0;
    val = PI / 180.0;
    ret = parseInt(Math.cos( x*val ));
    document.write("The cosine of " +
                           x + " is ");
    document.write(ret.toFixed(5));
    document.write(" degrees");
 
 
// This code contributed by shikhasingrajput
 
</script>


Output : 

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

 

Time complexity: O(1)
Auxiliary space: O(1)


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