Program for sum of cos(x) series - GeeksforGeeks

31 Mar, 2021
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++
Java
Python3
C#
PHP
Javascript
// 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){    // 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 Codeint main(){    float x = 50;    int n = 5;    cout << cosXSertiesSum(x, 5);    return 0;}
// Java program to find// the sum of cos(x) seriesimport java.lang.Math.*; class GFG{    static final double PI = 3.142;         static double cosXSertiesSum(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)(            cosXSertiesSum(x, 5) * 1000000) /                                 1000000.00);    }} // This code is contributed by Smitha.
# Python3 program to find the# sum of cos(x) series PI = 3.142; def cosXSertiesSum(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 Codex = 50;n = 5;print(round(cosXSertiesSum(x, 5), 6)); # This code is contributed by mits
// C# program to find the// sum of cos(x) seriesusing System; class GFG{    static double PI = 3.142;         static double cosXSertiesSum(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)(cosXSertiesSum(x, n) *                             1000000) / 1000000.00);    }} // This code is contributed by Smitha.
<?php// PHP program to find the// sum of cos(x) series $PI = 3.142; function cosXSertiesSum($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;$n = 5;echo cosXSertiesSum($x, 5); // This code is contributed by aj_36?>
<script> // Javascript program to find// the sum of cos(x) series const  PI = 3.142;     function cosXSertiesSum( 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( ((cosXSertiesSum(x, 5) * 1000000) / 1000000.00).toFixed(6)); // This code is contributed by shikhasingrajput </script>
0.642701
 
Note that we can also find cos(x) using library function.  
C++
C
Java
Python3
C#
PHP
Javascript
// 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 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 code to illustrate// the use of cos functionimport 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 code to illustrate# the use of cos functionimport 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# code to illustrate// the use of cos functionusing System; class GFG{     // Constant PI Declarationstatic double PI = 3.142; // Driver Codestatic 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 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?>
<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>
The cosine of 60.000000 is 0.500000 degrees
The cosine of 90.000000 is 0.000000 degrees
 
Smitha Dinesh Semwal
jit_t
Sanjit_Prasad
Mithun Kumar
SHUBHAMSINGH10
kumarv456
shikhasingrajput
series-sum
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