# Program for sum of cos(x) series

• Difficulty Level : Medium
• Last Updated : 30 May, 2022

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 ``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

 ``

## Javascript

 ``

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 ``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 ``#include ` `#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

 ``

## Javascript

 ``

Output :

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

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