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

Last Updated : 23 Jul, 2025

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

For sin function

Examples:  

Input : 90
Output : 1


{\displaystyle 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: 

1

Time Complexity: O(n)

Space Complexity: O(1)

For cos function

Examples:  

Input : 30
Output : 0.86602


{\displaystyle 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)


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