Program to calculate the value of sin(x) and cos(x) using Expansion

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Given a value of angle, you need to calculate Sin and Cos values corresponding to it.

For sin function

Examples:

Input : 90
Output : 1

$Sin(x)=\sum_{k=0}^{\infty } \frac {(-1)^k}{(2k+1)!}x^{2k+1}=x-\frac {x^3}{3!} + \frac {x^5}{5!} - .........$

C++

// CPP code for implementing sin function 
#include <iostream> 
#include <math.h> 
using namespace std; 
  
// Function for calculating sin value 
void cal_sin(float n) 
{     
    float accuracy = 0.0001, denominator, sinx, sinval; 
      
    // Converting degrees to radian 
    n = n * (3.142 / 180.0);  
  
    float x1 = n; 
      
    // maps the sum along the series 
    sinx = n;          
      
    // holds the actual value of sin(n) 
    sinval = sin(n);     
    int i = 1; 
    do
    { 
        denominator = 2 * i * (2 * i + 1); 
        x1 = -x1 * n * n / denominator; 
        sinx = sinx + x1; 
        i = i + 1; 
    } while (accuracy <= fabs(sinval - sinx)); 
    cout << sinx; 
} 
  
// Main function 
int main() 
{ 
    float n = 90; 
    cal_sin(n); 
    return 0; 
} 

Java

import static java.lang.Math.sin; 
  
// JAVA code for implementing sin function 
  
class GFG { 
  
// Function for calculating sin value  
static void cal_sin(float n)  
{      
    float accuracy = (float) 0.0001, denominator, sinx, sinval;  
      
    // Converting degrees to radian  
    n = n * (float)(3.142 / 180.0);  
  
    float x1 = n;  
      
    // maps the sum along the series  
    sinx = n;          
      
    // holds the actual value of sin(n)  
    sinval = (float)sin(n);      
    int i = 1;  
    do
    {  
        denominator = 2 * i * (2 * i + 1);  
        x1 = -x1 * n * n / denominator;  
        sinx = sinx + x1;  
        i = i + 1;  
    } while (accuracy <= sinval - sinx);  
       System.out.println(sinx);  
}  
  
// Main function  
  
  
    public static void main(String[] args) { 
        float n = 90;  
    cal_sin(n);  
      
    } 
} 

Python3

# Python3 code for implementing  
# sin function 
import math; 
  
# Function for calculating sin value 
def cal_sin(n): 
  
    accuracy = 0.0001; 
      
    # Converting degrees to radian 
    n = n * (3.142 / 180.0);  
      
    x1 = n; 
      
    # maps the sum along the series 
    sinx = n;      
      
    # holds the actual value of sin(n) 
    sinval = math.sin(n);  
    i = 1; 
    while(True): 
      
        denominator = 2 * i * (2 * i + 1); 
        x1 = -x1 * n * n / denominator; 
        sinx = sinx + x1; 
        i = i + 1; 
        if(accuracy <= abs(sinval - sinx)): 
            break; 
          
    print(round(sinx)); 
  
# Driver Code 
n = 90; 
cal_sin(n); 
      
# This code is contributed by mits 

C#

// C# code for implementing sin function  
using System; 
  
class GFG 
{ 
// Function for calculating sin value  
static void cal_sin(float n)  
{  
    float accuracy = (float) 0.0001,  
                      denominator, sinx, sinval;  
      
    // Converting degrees to radian  
    n = n * (float)(3.142 / 180.0);  
  
    float x1 = n;  
      
    // maps the sum along the series  
    sinx = n;      
      
    // holds the actual value of sin(n)  
    sinval = (float)Math.Sin(n);      
    int i = 1;  
    do
    {  
        denominator = 2 * i * (2 * i + 1);  
        x1 = -x1 * n * n / denominator;  
        sinx = sinx + x1;  
        i = i + 1;  
    } while (accuracy <= sinval - sinx);  
      
    Console.WriteLine(sinx);  
}  
  
// Driver Code 
static public void Main () 
{ 
    float n = 90;  
    cal_sin(n);  
} 
} 
  
// This code is contributed by jit_t 

PHP

<?php 
// PHP code for implementing sin function 
  
// Function for calculating sin value 
function cal_sin($n) 
{  
    $accuracy = 0.0001; 
      
    // Converting degrees to radian 
    $n = $n * (3.142 / 180.0);  
  
    $x1 = $n; 
      
    // maps the sum along the series 
    $sinx = $n;          
      
    // holds the actual value of sin(n) 
    $sinval = sin($n);  
    $i = 1; 
    do
    { 
        $denominator = 2 * $i * (2 * $i + 1); 
        $x1 = -$x1 * $n * $n / $denominator; 
        $sinx = $sinx + $x1; 
        $i = $i + 1; 
    } while ($accuracy <= abs($sinval - $sinx)); 
    echo round($sinx); 
} 
  
// Main function 
  
    $n = 90; 
    cal_sin($n); 
      
// This code is contributed by mits 
?> 

Javascript

<script> 
  
// javascript code for implementing sin function 
  
    // Function for calculating sin value 
    function cal_sin(n) { 
        var accuracy =  0.0001, denominator, sinx, sinval; 
  
        // Converting degrees to radian 
        n = n *  (3.142 / 180.0); 
  
        var x1 = n; 
  
        // maps the sum along the series 
        sinx = n; 
  
        // holds the actual value of sin(n) 
        sinval =  Math.sin(n); 
        var i = 1; 
        do { 
            denominator = 2 * i * (2 * i + 1); 
            x1 = -x1 * n * n / denominator; 
            sinx = (sinx + x1); 
            i = i + 1; 
        } while (accuracy <= sinval - sinx); 
        document.write(sinx.toFixed(0)); 
    } 
  
    // Main function 
  
      
        var n = 90; 
        cal_sin(n); 
  
  
// This code is contributed by todaysgaurav  
  
</script>

Output:

Time Complexity: O(n)

Space Complexity: O(1)

For cos function

Examples:

Input : 30
Output : 0.86602

$Cos(x)=\sum_{k=0}^{\infty } \frac {(-1)^k}{(2k)!}x^{2k}=1-\frac {x^2}{2!} + \frac {x^4}{4!} -.....$

C++

// CPP code for implementing cos function 
#include <iostream> 
#include <math.h> 
using namespace std; 
  
// Function for calculation 
void cal_cos(float n) 
{ 
    float accuracy = 0.0001, x1, denominator, cosx, cosval; 
      
    // Converting degrees to radian 
    n = n * (3.142 / 180.0); 
      
    x1 = 1; 
      
    // maps the sum along the series 
    cosx = x1;          
      
    // holds the actual value of sin(n) 
    cosval = cos(n); 
    int i = 1; 
    do
    { 
        denominator = 2 * i * (2 * i - 1); 
        x1 = -x1 * n * n / denominator; 
        cosx = cosx + x1; 
        i = i + 1; 
    } while (accuracy <= fabs(cosval - cosx)); 
    cout << cosx; 
} 
  
// Main function 
int main() 
{ 
    float n = 30; 
    cal_cos(n); 
}  

Java

// Java code for implementing cos function 
  
import static java.lang.Math.cos; 
  
class GFG { 
// Function for calculation 
  
static void cal_cos(float n) { 
    float accuracy = (float) 0.0001, x1, denominator, cosx, cosval; 
    // Converting degrees to radian 
    n = n * (float) (3.142 / 180.0); 
    x1 = 1; 
    // maps the sum along the series 
    cosx = x1; 
    // holds the actual value of sin(n) 
    cosval = (float) cos(n); 
    int i = 1; 
    do { 
        denominator = 2 * i * (2 * i - 1); 
        x1 = -x1 * n * n / denominator; 
        cosx = cosx + x1; 
        i = i + 1; 
          
    } 
    while (accuracy <= cosval - cosx); 
    System.out.println(cosx); 
      
} 
  
// Main function 
public static void main(String[] args) { 
    float n = 30; 
    cal_cos(n); 
      
} 
} 

Python3

# Python 3 code for implementing cos function 
  
from math import fabs, cos 
  
# Function for calculation 
def cal_cos(n): 
    accuracy = 0.0001
  
    # Converting degrees to radian 
    n = n * (3.142 / 180.0) 
      
    x1 = 1
      
    # maps the sum along the series 
    cosx = x1 
      
    # holds the actual value of sin(n) 
    cosval = cos(n) 
    i = 1
  
    denominator = 2 * i * (2 * i - 1) 
    x1 = -x1 * n * n / denominator 
    cosx = cosx + x1 
    i = i + 1
    while (accuracy <= fabs(cosval - cosx)): 
        denominator = 2 * i * (2 * i - 1) 
        x1 = -x1 * n * n / denominator 
        cosx = cosx + x1 
        i = i + 1
  
    print('{0:.6}'.format(cosx)) 
  
# Driver Code 
if __name__ == '__main__': 
    n = 30
    cal_cos(n) 
  
# This code is contributed by 
# Sahil_Shelangia 

C#

// C# code for implementing cos function  
  
using System; 
class GFG {  
// Function for calculation  
  
static void cal_cos(float n) {  
    float accuracy = (float) 0.0001, x1, denominator, cosx, cosval;  
    // Converting degrees to radian  
    n = n * (float) (3.142 / 180.0);  
    x1 = 1;  
    // maps the sum along the series  
    cosx = x1;  
    // holds the actual value of sin(n)  
    cosval = (float) Math.Cos(n);  
    int i = 1;  
    do {  
        denominator = 2 * i * (2 * i - 1);  
        x1 = -x1 * n * n / denominator;  
        cosx = cosx + x1;  
        i = i + 1;  
          
    }  
    while (accuracy <= cosval - cosx);  
    Console.WriteLine(cosx);  
      
}  
  
// Main function  
static void Main() {  
    float n = 30;  
    cal_cos(n);  
      
}  
}  
// This code is contributed by mits 

PHP

<?php 
// PHP code for implementing cos function 
  
// Function for calculation 
function cal_cos($n) 
{ 
    $accuracy = 0.0001; 
      
    // Converting degrees to radian 
    $n = $n * (3.142 / 180.0); 
      
    $x1 = 1; 
      
    // maps the sum along the series 
    $cosx = $x1;          
      
    // holds the actual value of sin(n) 
    $cosval = cos($n); 
    $i = 1; 
    do
    { 
        $denominator = 2 * $i * (2 * $i - 1); 
        $x1 = -$x1 * $n * $n / $denominator; 
        $cosx = $cosx + $x1; 
        $i = $i + 1; 
    } while ($accuracy <= abs($cosval - $cosx)); 
    echo round($cosx, 6); 
} 
  
// Driver Code 
$n = 30; 
cal_cos($n); 
  
// This code is contributed by mits 
?> 

Javascript

<script> 
  
// JavaScript code for implementing cos function 
  
// Function for calculation 
function cal_cos(n) 
{ 
    let accuracy = 0.0001, x1, denominator, cosx, cosval; 
      
    // Converting degrees to radian 
    n = n * (3.142 / 180.0); 
      
    x1 = 1; 
      
    // maps the sum along the series 
    cosx = x1;         
      
    // holds the actual value of sin(n) 
    cosval = Math.cos(n); 
    let i = 1; 
    do
    { 
        denominator = 2 * i * (2 * i - 1); 
        x1 = -x1 * n * n / denominator; 
        cosx = cosx + x1; 
        i = i + 1; 
    } while (accuracy <= Math.abs(cosval - cosx)); 
    document.write(cosx.toFixed(5)); 
} 
  
// Main function 
  
    let n = 30; 
    cal_cos(n); 
  
// This code is contributed by Surbhi Tyagi. 
  
</script>

Output:

0.86602

Time Complexity: O(n)

Space Complexity: O(1)

This article is contributed by Sakshi Tiwari. If you like GeeksforGeeks(We know you do!) and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
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Data Structures and Algorithms - Self Paced

Python Programming Foundation -Self Paced

Master Java Programming - Complete Beginner to Advanced