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 – (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 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 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) { // 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
# 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 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) { // 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 // 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 ?> |
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 ?> |
Output :
The cosine of 60.000000 is 0.500000 degrees The cosine of 90.000000 is 0.000000 degrees
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