Rad vs Deg accuracy



#2

I was wondering, I did the asin(acos(atan(tan(cos(sin(9)))))) and got 8.99999864267 of course. If I convert to 9 into Radians and do the same operation in RAD mode and convert the number back to degrees I get 9.00000000009. So the question is, why is the radians mode so much more accurate? Or am I missing something? If it is more accurate, why not just have the calc do all operations in Rad and just convert to and from degrees?


#3

Hi Rick,

1st of all, the supposed "accuracy" is a bit of a red herring here. You are effectively "pushing digits off a cliff" as you take these nested sin/cos/tan operations. So, it is not a real-life test of accuracy. In real life, you generally have most of the significant digits of your problem intact.

2nd, again in real life, you have so many sigfigs in the calculator, that it really doesn't matter which mode you choose, if an issue of truncation is occurring, it is at a far decimal place.

If you actually need all those places, then you are in a special league....

Regards,

Bill

#4

its because in deg mode, the machine is treating each of sin, cos and tan as degree arguments and performing deg->rad conversion for *each* one. then in each of atan, acos & asin its performing the opposite each time. whilst in rad mode there are no conversions except the first and final ones manually performed.

#5

It is two completely different calculations. sin(9) returns sine of 9 degrees or 9 radians, two very different numbers, and then you go on doing calculations on the result, interpreting angles as degrees or radians.

tan(cos(sin(9))) is meaningless because sin and cos does not return an angle in either degree or radian mode.

I think Valentin Albillo has pointed out that sin 9° = 0.1564, and cos 0.1564° is very close to 1, where all the meaningful digits are much smaller than 1 and get rounded off.

The same pathological case does not happen for the calculation in radians mode, because the numbers are completely different and in radians mode "less than one" is not the same as "very small".

#6

Here is Mike Sebastian's idea on using radians in the forensics algorithm.
http://www.rskey.org/~mwsebastian/miscprj/radians.htm


Possibly Related Threads...
Thread Author Replies Views Last Post
  How much accuracy does one actually need? Matt Agajanian 23 1,124 08-26-2013, 12:46 PM
Last Post: Kimberly Thompson
  Estimating accuracy in finite precision computations mpi 17 927 02-22-2013, 09:44 AM
Last Post: mpi
  WP 34S accuracy is excellent Jeff Johnson 15 737 06-01-2012, 10:41 PM
Last Post: Valentin Albillo
  50G precision & accuracy Matt Agajanian 11 623 05-17-2012, 11:15 AM
Last Post: Crawl
  Back with my DEG<->DMS formulas ! PGILLET 5 403 05-03-2012, 07:44 PM
Last Post: Bart (UK)
  Accuracy of Woodstocks Matt Agajanian 7 401 03-25-2012, 06:54 PM
Last Post: Eric Smith
  HP-35 Accuracy Threshhold Matt Agajanian 0 113 03-22-2012, 09:56 PM
Last Post: Matt Agajanian
  accuracy of integration and solve routines HP 15C LE Jan 3 265 02-02-2012, 01:03 PM
Last Post: Marcus von Cube, Germany
  Machine accuracy behaviour of the hp-35s and other models Mohammed Hadi 42 1,808 11-30-2009, 05:00 AM
Last Post: Herbert Crepaz (UK)
  Accuracy by chance Javier Goizueta 13 672 10-09-2009, 05:25 PM
Last Post: Gerson W. Barbosa

Forum Jump: