# CSharp - Write program to Calculate Sine function with Taylor expansion

## Requirements

You will write a program that calculates sine function with Taylor expansion.

## Hint

To perform the task, you can use a Taylor expansion.

The value of the sine function at a given point x (x is an angle in radians) can be calculated as a sum of infinite series.

```
x*x*x   x*x*x*x*x     x*x*x*x*x*x*x
sin x = x -    -------- + --------   +---------------+ ...
3!       5!            7!

```

7! = 1 * 2 * 3 * ... * 7.

## Demo

```using System;
class Program//from w  w  w  .jav  a2  s  .c om
{
static void Main(string[] args)
{
// Input
Console.Write("Enter an angle in degrees: ");
string input = Console.ReadLine();
double angle = Convert.ToInt32(input);

// Converting to radians
double x = Math.PI / 180 * angle;

// Preparations
double member;
double sum = 0;
double tinyValue = 1e-15;

double sign = 1;
double power = x;
double factorial = 1;
double multiplier = 1;

// Sum of the series
do
{
// Calculating current member of the series
member = sign * power / factorial;

// Appending to sum
sum += member;

// Preparing next step
sign *= -1;
multiplier++;
factorial *= multiplier;
multiplier++;
factorial *= multiplier;

power *= x * x;

} while (Math.Abs(member) > tinyValue);

// Output
Console.WriteLine("Our value: " + sum.ToString());
Console.WriteLine("Math.Sin:  " + Math.Sin(x).ToString());

}
}
```