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 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
Time complexity: O(1)
Auxiliary space: O(1)
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
Time complexity: O(1)
Auxiliary space: O(1)