# 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++

 `// CPP program to find the  ` `// sum of cos(x) series ` `#include ` `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

 ` `

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 ` `#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

 ` `

Output :

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

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