# Program for sum of cos(x) series

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 – (x^{2} / 2 !) + (x^{4} / 4 !) – (x^{6} / 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 = 45Output :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

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