Trig Ratios: What Function Does "sin(x)" Represent?

[Gaz031]

I've been working with the trigonometric ratios for a long time now and was wondering, when you type sin(x), where x is any number and hit the equals sign, what function is actually being applied to the number?

 

[humanino]

I guess that would be
\sin(x)=\sum_n \left( \frac{x^{4n+1}}{(4n+1)!}-\frac{x^{4n+3}}{(4n+3)!} \right)
to finite order, by first reducing to the fundamental [-\pi;\pi]

 

[HallsofIvy]

For a very long time, I thought that calculators (and computers) used the Taylor's series (what humanino gives is a variation on that) for e^x, sin(x), cos(x), etc. but I have been informed that all modern calculations use the "CORDIC" algorithm.

Here is a link to an explanatory website:
http://www.dspguru.com/info/faqs/cordic.htm

 

[humanino]

now, that's clever ! Anyway, I had doubt about the series. Thanks Hallsoflvt. This algorithm makes me thinf of FFT.
edit:
(well actually it is much simpler)

 

[Gaz031]

Interesting, thanks.