CORDIC in Degrees vs. Radians  Printable Version + HP Forums (https://archived.hpcalc.org/museumforum) + Forum: HP Museum Forums (https://archived.hpcalc.org/museumforum/forum1.html) + Forum: Old HP Forum Archives (https://archived.hpcalc.org/museumforum/forum2.html) + Thread: CORDIC in Degrees vs. Radians (/thread188486.html) 
CORDIC in Degrees vs. Radians  Mike Fikes  07232011 On a Voyager (15C) in degrees mode, cos 60 = 0.5. The same is true for a Pioneer (20S). If, instead, this is performed in radians mode, first converting 60 degrees to radians using >RAD, this results in
15C: 0.5000000002 My question: How do these machines produce exactly the right answer when in degrees mode?
Is CORDIC internally performed always either degrees or radians (with the necessary conversions of input being done first)? Or is it internally performed using the mode that the calculator is set to?
Re: CORDIC in Degrees vs. Radians  Gerson W. Barbosa  07232011 HP calculators round the answer to the number of digits of the display. Thus, on the 32SII 60 > RAD returns 1.04719755120, a worst approximation to pi/3 than 1.04719755119660 which would be used internally when in DEG mode. In RAD mode the internal results are cos(1.04719755120 rad) = 0.499999999997054or 0.499999999997respectively, when rounded to 12 digits. Gerson.
Re: CORDIC in Degrees vs. Radians  Mike Fikes  07232011 Is the following accurate?
When in degrees mode, the 15C internally converts the input to a radians representation that employs guard digits (in other words, a representation with more than 10 digits), which is then passed to the CORDIC routine. The (greater than 10digit) output of CORDIC is then rounded to the 10 digits of the display.
Re: CORDIC in Degrees vs. Radians  Gerson W. Barbosa  07232011 Yes, I think things occur like that. These past threads might be of interest to you: http://www.hpmuseum.org/cgisys/cgiwrap/hpmuseum/archv016.cgi?read=103151 http://www.hpmuseum.org/cgisys/cgiwrap/hpmuseum/archv016.cgi?read=103356 http://www.hpmuseum.org/cgisys/cgiwrap/hpmuseum/archv014.cgi?read=62301
Edited: 23 July 2011, 2:37 p.m.
Re: CORDIC in Degrees vs. Radians  Mike Fikes  07232011 Yep, post #16 in the first thread you referenced indicated the following with respect to trig in degree mode on the 15C:
Quote:
Thanks :)
Re: CORDIC in Degrees vs. Radians  Eric Smith  07242011 It is possible to do CORDIC operations in degrees, grads, or other angular units, but generally HP calculators don't do that. They internally convert to radians. As Gerson has noted, they use extra digits in internal calculations to get a more accurate result than if you did the conversion from the keyboard.
I say "generally" because I have no idea how models like the 6s, 8s, 9s, 9g, and 30s work internally.
