Sin Cos And Tan

[sgm]

See Sir Robin's second-to-last post. Nice link though.

[CoBB]

[thornahawk]

This needs to be moved into the "Math and Science" forum. Can someone be so kind? :)

thornahawk

[DarkerLine]

Done. Now everyone will find out about the topic in which I double-posted. And I've tried so hard to cover it up...

[thornahawk]

Thank you, DarkerLine. Don't worry, I don't think anyone would begrudge you the multiple post. ;)

Now, since I have done the dirty job of resurrecting the thread, I'd think of trying to add something substantial to this wonderful discussion (belated as it may be).

For starters, the comment re: power series is close, but no cigar. The problem with power series is that the tend to be very accurate only at the center of expansion (i.e. the origin), at the expense of inaccuracy at points so far away.

We first recall symmetries: sine and tangent are odd: sin(x) = -sin(-x), whilst cosine is even: cos(-x) = cos(x). These reflection formulae reduce the problem to evaluating at positive arguments.

We then remember that the trig functions are periodic: sin(x + 2π) = sin(x), and similarly for the cosine and tangent, except that the period is π rather than 2π for tan(). Hence, by subtracting appropriate multiples of the period, the problem reduces to evaluating over a preset range.

Here's the meat: TI apparently uses the so-called CORDIC algorithm, whose discussion I can do no better than point the curious to http://www.cnmat.berkeley.edu/~norbert/cordic/node4.html . If questions still remain, I will be happy to answer them. :)

thornahawk

P.S. Other machines use the so-called "economized Chebyshev approximation", which is effectively replacing the terms of the corresponding power series with appropriate combinations of the Chebyshev polynomials. Google on them for more info.