How can I write my own sinus function?

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I just want to write my own sinus function to realise how does it work.

What I have tried:

I've tried to write this using C++. And I found Taylor series.

C++

long double sinus(double x)
{
	long double result = 0.0;
	for (int i = 0; i < 100; i++)
	{
		result += (pow(-1, i - 1)*pow(x, 2 * i - 1)) / Factorial(2 * i - 1);
	}	
	return result;
}

It is my function and it returns wrong results(Factorial function works correctly).

Posted 22-Jan-21 20:39pm

temchik_ggg

Updated 22-Jan-21 23:59pm

CPallini

v2

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Comments

Christian Graus 23-Jan-21 2:44am

Do you mean sine? If your result is wrong, your algorithm is wrong

KarstenK 23-Jan-21 4:49am

yes you can, but using the built in functions are bullet proof and long used, so use them and implement your own features.

2 solutions

Solution 1

See answer here: c++ - Sine Function without any library - Stack Overflow[^]

Posted 22-Jan-21 20:53pm

RickZeeland

Comments

CPallini 23-Jan-21 12:36pm

5.

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OriginalGriff · Accepted Answer · 2021-01-22T21:12:00

The Taylor series for sin(x) is simple:

sin(x) = pow(x, 1) - pow(x, 3) / 3! + pow(x, 5) / 5! - ...

But your implementation does two things: starts with -1 instead of 1, and makes it look a lot more complex than it needs to be. If you don't believe me, work out each term in a short series manually (4 or 5 terms should do) and use the debugger to look at the equivalent terms your code is generating!

Here's a simple implementation in C#:

C#

static double sin(double x)
    {
    double result = 0.0;
    double sign = 1.0;
    for (double power = 1.0; power <= 20.0; power += 2, sign = -sign)
        {
        result += sign * (Math.Pow(x, power) / factorial(power));
        }
    return result;
    }
static double factorial(double n)
    {
    double result = 1.0;
    while (n > 1.0)
        {
        result *= n;
        n -= 1.0;
        }
    return result;
    }

Which gives a result accurate to at least 5 decimal places despite using a much, much shorter series that you do!

You may also need to remember when testing that the Taylor series works in Radians, not Degrees!