atan2 formula..

[Downsider]

Okay; For reasons, I'd like to know the formula for atan2.

Thanks in advance.

[helios]

Good luck. It's usually implemented in hardware. I'm still trying to find how to manually calculate the sine of an angle.

[Duthomhas]

Y'all are kidding, right?

atan2
http://en.wikipedia.org/wiki/Atan2
x87 fpu opcode: FPATAN
http://www.ews.uiuc.edu/~cjiang/reference/vc107.htm

sine
http://en.wikipedia.org/wiki/Trigonometric_functions#Sine
x87 fpu opcode: FSIN
http://www.ews.uiuc.edu/~cjiang/reference/vc115.htm

[Downsider]

Cool, thanks. I knew how to do sine and the like but I was unsure about atan2.

[helios]

The sine section in Wikipedia doesn't actually explain how to calculate the length of the opposite side, it just says sine is the ratio between that length and the hypotenuse.
Neither does the other link.

EDIT: Never mind. Taylor polynomial of degree 7 ftw.

[Duthomhas]

You've lost me with the Taylor series.

The sine is nothing more than the ratio of two scalars: opposite / hypotenuse. Sine will not give you those values --you have to know them in advance. The inverse sine gives you the value of the angle (since sin^-1 is not bijective, the domain and range are usually restricted to [-1,1] and [-^π/₂,^π/₂]). The inverse sine is usually calculated in computers using a lookup table.

What exactly is it that you are trying to calculate?

[helios]

What I'm looking for is a way to, for a hypotenuse of 1 and an angle x, calculate the lengths of the adjacent side and the opposite side.
This gives me a pretty close approximation:

double taylor7(double x){
	return x - pow(x,3)/6 + pow(x,5)/125 - pow(x,7)/5040;
}

[Duthomhas]

Given:

/|
/ |
1/ | y
/ _|
/) | |
A-----+
x


sin A = ^y/₁ --> 1 × sin A = y --> sin A = y

cos A = ^x/₁ --> 1 × cos A = x --> cos A = x

I still don't think I understand what it is that you are trying to compute.

[helios]

I think we're saying the same thing in two different languages, while both speaking English at the same time.

I know about sin() and I know that I can get that value from sin(). BUT what I was interested in was a function that gave equivalent results. I.e. calculate the sine without using sin(). A replacement for sin(), so to speak.
I don't think there's such a mathematical function, however.