Program for sum of cos(x) series
Last Updated :
20 Feb, 2023
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 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 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# 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 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
?>
<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>
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 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 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 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# 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 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
?>
<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)
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