OT: Cosine curio - Printable Version +- HP Forums (https://archived.hpcalc.org/museumforum) +-- Forum: HP Museum Forums (https://archived.hpcalc.org/museumforum/forum-1.html) +--- Forum: Old HP Forum Archives (https://archived.hpcalc.org/museumforum/forum-2.html) +--- Thread: OT: Cosine curio (/thread-206765.html) |
OT: Cosine curio - Bob Patton - 12-11-2011 Laguerre cosine approximation<*** End of File ***> Re: OT: Cosine curio - Crawl - 12-11-2011 It seems like the final 1 should be positive, not negative.
Re: OT: Cosine curio - Namir - 12-12-2011 Interesting approximation! Can we enhance it now that we have tools like Matlab and Excel? Crawl it right in pointing out that the trailing -1 in the first two equations should be +1.
Namir
Re: OT: Cosine curio - C.Ret - 12-13-2011 Really interesting approximation. As Namir and Crawl have already point out, there is a typo in the developed formulae only.
The linear formulea and the RPN instructions are all correct. Using my HP-41C, I just test a few points to observe error between cosine and the Laguerre approximation (express in the following table as ppm
Angle(°) m=a/90° Laguerre(m) Cos(a) Error(ppm) As explain, in first quadrant, few error and exact value for same remarkable values are obtained. No more approximation can be obtained after 180° due to the sign of the polynôme under the square root. The following figure better illustrate accuracy and region of interest for this cosine approximation: Note that in this graph, Lag(a) is the real part of the laguerre approximation. That’s why plot continue after the 180° limit. As Namir point it out, we can enhance this approximation, but not only in accuracy, other way may be to make it usable on a larger domain.
Edited: 13 Dec 2011, 5:58 a.m.
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