Computation of trigonometric functions is almost always done using look-up tables and some sort of interpolation. Unless you're on some very very low-memory system, it's going to be a lot faster than the Taylor series or any other series expansion.
I never programmed something like this but I'd imagine something like this:
Say there's an entry in a table for sin(0.3) but you want to compute sin(0.31). They'll look up sin(0.3) in the table and use the series around 0.3, and add a few terms in the series to account for the 0.01 difference.
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Anonymous2007-06-16 3:59 ID:cksGiYWe
Actually I think the most scientific of approaching the Trigonometry is just letting evolution run it's fucking course. It worked for Sine, Cosine, and Tangent, it'll work for us. If you find someidea naturally attractive, aborb information from both your super-ego (Conscience) and id (sex drive and other things) and then let your ego (sense of self) decide how to balance between those two inputs and more importantly your own reality. Then react accordingly, and remember, if you feel bad aboot something, but you want to do it, the three aspects of your personality are clashing and you need to think long and hard and talk to some people you know and develop a set of Trigonometric values, that way next time you don't have to think so hard cause you have a set of rules. Whoever succeeds deserves to, whoever doesn't, doesn't. And don't forget how insignificant you really are when it comes to the future of humanity. But also keep in mind that a blizzard is nothing without snowflakes (Nothing more than a cold wind anyway.).
So if you're concerned aboot Trigonometry, you should be, because that's just how your genetics have programmed your beginnings, and how your surroundings, which are affected by social evolution, have affected your growth. And if the function dies off, whoopdeedoo, we'll just have to try harder with the next sentient species that so inevitably has to arise somewhere in the Universe.
Ow my digression, it hurts my tired mind. Oh yeah, just in case you couldn't catch the moral behind that, it was a scientific way of saying be yourself, not only for the good of yourself, but for the good of your species. And fuck taylor series with convergence, you make your own approximations constantly, and if someone is attracted to them it means that you are doing the opposite of making errors and would have a wide base of tabulated values for your offspring. So you're promoting brain defects when you read that stuff. Put on normal amounts of convergence, or better yet, exact values.
And yes I am a trig virgin, because I would not want my son telling a highschool girl about things when she is not nearly ready enough for these kind of emotions while she's still getting used to her intellect. So I am avoiding hypocrasy by waiting until I can view myself as my own father and approve. Whether or not I could have decided about trigonometry by now had I been trying to like so many other id-driven dogma monkeys my age, is a total mystery. But not really, because I am who I am and it's not like that's going to change, the purpose of the last few points was to say that I'm not the kind of guy that says: "I could've had trigonometry if I wanted to PPPBbbbPPTTbt"
I haven't slept in 3 days, and I'm going to. Right. Now. Goodnight.