3 replies to this topic

[jungingj]

I bought a new Casio FX-991EX today and tried to calculate some simple trigonometric functions.
 
When given:

 

       1. x=pi/6 (In Rad):

 

          16*cos(x)^6 - 8*cos(x)^4 - 16*cos(x)^4 + 10*cos(x)^2 - cos(x)^2
 
          the result is:
          
          -1.8*10^(-13)
 
       2. x=pi/6 (In Rad):
 
           16*[cos(x)^4]*[cos(x)^2] - 8*cos(x)^4 - 16*cos(x)^4 + 10*cos(x)^2 - cos(x)^2
 
           the result is:
          
           0
 
       3. x=pi/6 (In Rad):
 
           16*cos(x)^6 - 8*cos(x)^4 - 16*cos(x)^4 + 9*cos(x)^2
 
           the result is:
          
           0
 
The true value is 0.
All three expression are equivalent from the algebraic point of view.
I got the same results when I put x=30 (In Deg), so it is not Deg/Rad problem.
I got the same results when I used the FX-82ES.
I do not own anymore scientific calculators so I can not investigate this issue further. 
 
I know that in this forum there are people that are more expert in Casio calculators than I am. 
I want to hear your opinions.
thanks.

Edited by jungingj, 16 October 2017 - 05:00 PM.

[anon34]

Those calculator use binary-coded floating point with 15 decimal digits of accuracy, so numerical errors are unavoidable.

Edited by user202729, 17 October 2017 - 08:04 AM.

[pan.gejt]

I tried the 1st expression

 

a ) TI-30X Pro ( equivalent of Casio fx-991 derivates) - computing is not possible due to entry-limit (no additional characters can be entered)

b ) HP-35s: 9×10^-12

c ) Sharp EL-W506X: 0

Two graphic calcs

d ) TI-84 Plus CE-T - the result is 0

e ) Casio fx-CG50 - the result is 0

 

So the conclusion is the result has nothing to do with specific calculator brands, but rather with numeric precision (accuracy) on cheaper calcs. It seems it's HW related together with implemented algorithms.

Edited by pan.gejt, 18 October 2017 - 06:34 PM.

[frankmar98]

Tested on my CFX-9970G (top of the range Casio calculator in 1999): 

 

-1.7E+1

 

If I put the parenthesis like this (cos 30)^4 instead of cos(30)^4, the result is:

 

0.0000 (Sci4 mode)

 

The old linear input of the CFX and AFX series is different than the new calcs inputs. If you add a function, the calculator won't add parenthesis, a function without parenthesis has more priority than exponents, but less priority than parenthesis.