Casio fx-CG50 - Hyperbolic functions of complex numbers
02-29-2020, 02:28 AM (This post was last modified: 02-29-2020 02:35 AM by Dands.)
Post: #1
 Dands Member Posts: 59 Joined: Jul 2015
Casio fx-CG50 - Hyperbolic functions of complex numbers
Hello,

I recently discovered that my CG50 can't evaluate hyperbolic functions of complex numbers such as

cosh(2*i)

or

sinh(2+2*i)

Giving me a "Non-real ERROR".

It's important to point out that other calculators such as the HP Prime and TI Nspire can do this with no problem. If you're asking yourself why I need this: calculating impedance parameters of power distribution lines.

I tried both rad and deg modes and my calculator is in Complex mode. Latest OS installed.

Any ideas on how why this isn't working? It's a shame because I really expected this calculator to do this.

Thanks
02-29-2020, 05:58 AM (This post was last modified: 02-29-2020 06:03 AM by Steve Simpkin.)
Post: #2
 Steve Simpkin Senior Member Posts: 1,067 Joined: Dec 2013
RE: Casio fx-CG50 - Hyperbolic functions of complex numbers
(02-29-2020 02:28 AM)Dands Wrote:  Hello,

I recently discovered that my CG50 can't evaluate hyperbolic functions of complex numbers such as

cosh(2*i)

or

sinh(2+2*i)

Giving me a "Non-real ERROR".

It's important to point out that other calculators such as the HP Prime and TI Nspire can do this with no problem. If you're asking yourself why I need this: calculating impedance parameters of power distribution lines.

I tried both rad and deg modes and my calculator is in Complex mode. Latest OS installed.

Any ideas on how why this isn't working? It's a shame because I really expected this calculator to do this.

Thanks

In looking at Appendix 2 (Input ranges) of the fx-CG50 Software User's Guide, it appears that the CG50 will accept complex numbers for a number of functions (log, powers, roots, etc) but not for any trig functions.

One way around this limitation is to install Bernard Parisse's excellent port of Xcas for the fx-CG50 named KhiCAS. More information and documentation is available at: https://www.cemetech.net/forum/viewtopic...88&start=0

Once you install KhiCAS, you can evaluate cosh(2*i) for an answer of -.41614837 or sinh(2+2*i) for an answer of -1.50930649+3.42095489*i in that environment (rad).
Tip: press the "S<->D" key first to enter "approx(" before typing in "cosh(2*i))" to get a decimal answer.

Of course this is also a full featured CAS much like the one available on the Prime [ I wonder why ] so it can do a lot more than just these examples.
02-29-2020, 08:37 AM (This post was last modified: 02-29-2020 08:38 AM by Dands.)
Post: #3
 Dands Member Posts: 59 Joined: Jul 2015
RE: Casio fx-CG50 - Hyperbolic functions of complex numbers
(02-29-2020 05:58 AM)Steve Simpkin Wrote:  In looking at Appendix 2 (Input ranges) of the fx-CG50 Software User's Guide, it appears that the CG50 will accept complex numbers for a number of functions (log, powers, roots, etc) but not for any trig functions.

One way around this limitation is to install Bernard Parisse's excellent port of Xcas for the fx-CG50 named KhiCAS. More information and documentation is available at: https://www.cemetech.net/forum/viewtopic...88&start=0

Once you install KhiCAS, you can evaluate cosh(2*i) for an answer of -.41614837 or sinh(2+2*i) for an answer of -1.50930649+3.42095489*i in that environment (rad).
Tip: press the "S<->D" key first to enter "approx(" before typing in "cosh(2*i))" to get a decimal answer.

Of course this is also a full featured CAS much like the one available on the Prime [ I wonder why ] so it can do a lot more than just these examples.

WOW! This is really amazing! Thank you so much for the quick answer. It's definitely a great solution for what I need.

It would be amazing if it integrated with the run-matrix mode. Do you know if there's a way to save the most used functions, say cosh, so that it's easier to access? It seems that I always have to find it in the list or type it.

Also, is there a way to show the decimal approximation by default instead of always using approx() before the functions?

Thanks again!
02-29-2020, 05:00 PM
Post: #4
 ijabbott Senior Member Posts: 1,277 Joined: Jul 2015
RE: Casio fx-CG50 - Hyperbolic functions of complex numbers
I suppose you could use the identities $$\sinh(z) = \frac{e^z - e^{-z}}{2}$$, $$\cosh(z) = \frac{e^z + e^{-z}}{2}$$, $$\tanh(z) = \frac{e^z - e^{-z}}{e^z + e^{-z}}$$, etc. - but it would be nicer if they were built in!

— Ian Abbott
02-29-2020, 05:02 PM
Post: #5
 Dands Member Posts: 59 Joined: Jul 2015
RE: Casio fx-CG50 - Hyperbolic functions of complex numbers
(02-29-2020 05:00 PM)ijabbott Wrote:  I suppose you could use the identities $$\sinh(z) = \frac{e^z - e^{-z}}{2}$$, $$\cosh(z) = \frac{e^z + e^{-z}}{2}$$, $$\tanh(z) = \frac{e^z - e^{-z}}{e^z + e^{-z}}$$, etc. - but it would be nicer if they were built in!

Yeah these work but are one extra step in my lengthy calculations. I agree those should be built in. I wish Casio had a channel for users to request future OS updates. Thanks
02-29-2020, 08:03 PM
Post: #6
 Steve Simpkin Senior Member Posts: 1,067 Joined: Dec 2013
RE: Casio fx-CG50 - Hyperbolic functions of complex numbers
(02-29-2020 08:37 AM)Dands Wrote:
(02-29-2020 05:58 AM)Steve Simpkin Wrote:  In looking at Appendix 2 (Input ranges) of the fx-CG50 Software User's Guide, it appears that the CG50 will accept complex numbers for a number of functions (log, powers, roots, etc) but not for any trig functions.

One way around this limitation is to install Bernard Parisse's excellent port of Xcas for the fx-CG50 named KhiCAS. More information and documentation is available at: https://www.cemetech.net/forum/viewtopic...88&start=0

Once you install KhiCAS, you can evaluate cosh(2*i) for an answer of -.41614837 or sinh(2+2*i) for an answer of -1.50930649+3.42095489*i in that environment (rad).
Tip: press the "S<->D" key first to enter "approx(" before typing in "cosh(2*i))" to get a decimal answer.

Of course this is also a full featured CAS much like the one available on the Prime [ I wonder why ] so it can do a lot more than just these examples.

WOW! This is really amazing! Thank you so much for the quick answer. It's definitely a great solution for what I need.

It would be amazing if it integrated with the run-matrix mode. Do you know if there's a way to save the most used functions, say cosh, so that it's easier to access? It seems that I always have to find it in the list or type it.

Also, is there a way to show the decimal approximation by default instead of always using approx() before the functions?

Thanks again!

Unfortunately I don't see a quick shortcut for entering the hyperbolic functions. I have been pressing the normal trig key (sin, cos, tan, etc) then left cursor, F5 (A<->a), h, Alpha (to turn off Alpha lock), right cursor. Not very elegant.

I also don't see a way to force approximate answers without entering the "approx(" first. At least there is a shortcut key for that (S<->D). I suspect since Xcas is typically used to find exact answers, a persistent approximate mode was not seen as important. You could *normally* use the Run-Matrix mode for that. There is also the fact that, due to memory size limitations for Casio apps (2MB), Bernard had to cut back on the features included in KhiCAS. This may also explain why you can't share results outside of the KhiCAS environment. By design, it is like a separate calculator.

KhiCAS has a lot of features! Read the 20 posts in the cenetech.net link I provided and look at the documentation link in Bernard's first post for more information.
02-29-2020, 09:30 PM (This post was last modified: 02-29-2020 09:31 PM by Dands.)
Post: #7
 Dands Member Posts: 59 Joined: Jul 2015
RE: Casio fx-CG50 - Hyperbolic functions of complex numbers
(02-29-2020 08:03 PM)Steve Simpkin Wrote:  Unfortunately I don't see a quick shortcut for entering the hyperbolic functions. I have been pressing the normal trig key (sin, cos, tan, etc) then left cursor, F5 (A<->a), h, Alpha (to turn off Alpha lock), right cursor. Not very elegant.

I also don't see a way to force approximate answers without entering the "approx(" first. At least there is a shortcut key for that (S<->D). I suspect since Xcas is typically used to find exact answers, a persistent approximate mode was not seen as important. You could *normally* use the Run-Matrix mode for that. There is also the fact that, due to memory size limitations for Casio apps (2MB), Bernard had to cut back on the features included in KhiCAS. This may also explain why you can't share results outside of the KhiCAS environment. By design, it is like a separate calculator.

KhiCAS has a lot of features! Read the 20 posts in the cenetech.net link I provided and look at the documentation link in Bernard's first post for more information.

That's a great way to do it indeed, just use the shortcut for sin and cos and add an 'h'. I like it.

I also believe that it was not meant to show approximations right away. Parisse stated that "There is no auto-simplification in KhiCAS, except for fractions of integers.".

A feature I'd love to see would be to be able to paste results to the run matrix mode. It seems to be not possible right now.

Thanks again for all your help Steve.
03-01-2020, 04:54 AM
Post: #8
 Eddie W. Shore Senior Member Posts: 1,540 Joined: Dec 2013
RE: Casio fx-CG50 - Hyperbolic functions of complex numbers
(02-29-2020 05:00 PM)ijabbott Wrote:  I suppose you could use the identities $$\sinh(z) = \frac{e^z - e^{-z}}{2}$$, $$\cosh(z) = \frac{e^z + e^{-z}}{2}$$, $$\tanh(z) = \frac{e^z - e^{-z}}{e^z + e^{-z}}$$, etc. - but it would be nicer if they were built in!

Agree to both of your points
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