cos(x)系列和的程序

给定n和x，其中n是序列中的项数，x是角度的度数。
程序使用级数展开公式计算x的余弦值，并将该值与库函数的输出进行比较。

使用的公式：
COS X = 1 – ^{(！×2/2)+(X4分之4！)} – (X6^分之6！)+ …

例子 ：

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)
{
    // 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.

Javascript

 
// Javascript program to find
// the sum of cos(x) series
 
const  PI = 3.142;
 
    function 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);
 
        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( ((cosXSertiesSum(x, 5) * 1000000) / 1000000.00).toFixed(6));
 
// This code is contributed by shikhasingrajput
 

输出 ：

0.642701

注意，我们也可以使用库函数找到cos(x)。

C++

// C++ code to illustrate
// the use of cos function
#include 
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 
#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

Java脚本

 
// 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
 

输出 ：

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