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HP 35s and Cosine of large numbers - 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: HP 35s and Cosine of large numbers (/thread-145694.html) |
HP 35s and Cosine of large numbers - Chuck - 01-13-2009 I've searched the archive and came up with several discussions of the log bug using large numbers, but didn't find anything about trig functions of large numbers. In particular, try taking the cosine of : 2pi x10^8Things start to break down around 8 and 9, and become totally unpredictable beyond 11. The TI8x series skirts this issue by giving a domain error for anything beyond 1x10^11. Granted, there may be no practical purpose for arguments of this magnitude, but still is amusing, if not alarming. Apologies if this has already been beaten to death. If so, I must have been asleep at the wheel.
CHUCK
Re: HP 35s and Cosine of large numbers - Michael - 01-13-2009 Hello,
Edited: 13 Jan 2009, 6:28 p.m.
35s...Cosine of large numbers - Hal Bitton in Boise - 01-14-2009 Interesting... Re: HP 35s and Cosine of large numbers - Karl Schneider - 01-14-2009 Hi, Chuck --
Quote: Of course, these calculations should be assumed in radians mode, and the answer should always be unity as long as pi is exact. However, this is not the case unless pi is treated symbolically. Accuracy of the input-argument angle is limited by the 12 significant digits; there is absolutely no fractional part left after being "consumed" by a power-of-10 multiplier of 11 or greater.
Quote: Nothing for the HP-35s, but two discussions took place in 2007 on this topic. Both links point to a post of mine, but you can review the entire or pertinent threads:
Trigonometrics for Really Big Input
-- KS Edited: 14 Jan 2009, 3:42 a.m.
Math Curiousity...an old fashioned approach - Hal Bitton in Boise - 01-14-2009 Hi Karl Quote:I can't get my 50G to return unity for the expression cos(2pi*1.E12), even though it appears to be carrying pi symbollically. It seems that 1E12 becomes the non integer value 1.E12 when entered (as evidenced by the decimal point). Therefor when I evaluate the expression, the calc switches to approx mode, and returns .9157108. The CAS setting "Simp non rationals" has no effect. Any insight on this? Best regards, Hal Re: Math Curiousity...an old fashioned approach - Karl Schneider - 01-15-2009 Quote: Hal -- I'm no expert on RPL, but I have an HP-49G that performs similarly. Pi is approximated by a 12-digit value when "->NUM" is executed. Evaluating 'SIN(pi)' on the HP-49G yields -2.0661537357E-13, just as on an HP-42S, where this is done numerically. EXACT mode may apply only to integers, which allows (for example) every digit of 60! to be calculated. -- KS
Edited: 15 Jan 2009, 12:59 a.m.
I think I found a way - Hal Bitton in Boise - 01-15-2009
Quote: Indeed Karl...The same result I get, unless I leave pi in symbolic form, in which case Sin(symbolic pi) evaluated to zero. My quandary had been how to get the calculator to treat exponents of 10 entered with the EEX key as exact integers, which would seem a logical thing, but which apparently it will not do. I think I have found a workaround, however. Once the expression is entered, use the ->Q function to convert it to an exact integer. Then the calc will treat the entire expression symbolically, with the expected ideal results. For example: key in 2*(symbolic pi)*1.0E12 (using the EEX key) , and execute ->Q, which will return: 2*(symbolic pi)*1000000000000 Now, take the cosine of this, and eval, and low and behold, the much sought after unity is returned. The accuracy does not degrade with bigger coefficients, either...2*(symbolic pi)*1.0E450 ->Q COS EVAL returns 1. Best regards, Hal |