[cas] use of functions hyperbolic secant and cosecant and inverses
06-08-2016, 11:57 AM (This post was last modified: 06-13-2016 12:04 PM by compsystems.)
Post: #1
 compsystems Senior Member Posts: 1,202 Joined: Dec 2013
[cas] use of functions hyperbolic secant and cosecant and inverses
why not to included the hyperbolic secant and cosecant and inverses?

high school algebra books and first levels of engineering the show.
these elementary functions must be in the system built-in.

that you think, are important SECH() and CSECH() in engineering and education? other CAS include them, why not xcas?

It would also allow display outputs rewritten or simplified
https://www.wolframalpha.com/input/?i=di...h(x%2F2)))

with SECH() and CSECH()
diff (2* atan(tanh(x/2))) -> sech(x)

int(sech(x)) -> (2* atan(tanh(x/2)))

current CAS, WITHOUT SECH() and CSECH()

diff (2* atan(tanh(x/2))) -> (-tanh((x/2))^2+1)/(tanh((x/2))^2+1)

https://en.wikipedia.org/wiki/Inverse_hy...c_function
08-03-2017, 07:35 AM
Post: #2
 math7 Member Posts: 163 Joined: Feb 2017
RE: [cas] use of functions hyperbolic secant and cosecant and inverses
Correct, it would be a good thing to incorporate it into the CAS because it would simplify many expressions that currently contain longer functions, and when using these hyperbolic functions, much used indeed in complex variable, the expressions would be simpler and shorter.
08-03-2017, 11:41 PM (This post was last modified: 08-03-2017 11:50 PM by matthiaspaul.)
Post: #3
 matthiaspaul Senior Member Posts: 385 Joined: Jan 2015
RE: [cas] use of functions hyperbolic secant and cosecant and inverses
I agree, the Prime should support these (and other missing trigonometric and) hyperbolic functions and their inverses (as well). See also:

They would all be straight-forward to implement.

There's one potential issue, though: It depends on the locale if these functions are part of the curriculum, so for a device used in schools, there should be some user-selectable way to suppress the calculator returning results in terms of these functions and instead to return results in terms of sin(), cos(), and tan() only. Otherwise the system might happen to give a short answer in f.e. sec() or exsec() to pupils who were never taught these functions and would prefer an answer in terms of cos(), even if it would be longer. This could be solved by adding something like a "suppress" flag to each (such) function which can be enabled or disabled individually. Say, if a user doesn't want answers in exsec(), s/he could set the suppress flag for exsec() and the system would avoid utilizing this function and fall back to use cos() instead. Enabling or disabling several of these flags at once could be done using profiles. (This idea is similar to how built-in commands can be individually enabled or disabled in some advanced command line interpreters like TC/4NT/4OS2/4DOS: For example SETDOS /I-TOUCH would disable the internal TOUCH command in 4DOS so an external TOUCH utility could be used instead of having to specify paths or having to rename it. SETDOS /I+TOUCH would reenable the internal TOUCH command again later on. You get the idea...)

Greetings,

Matthias

--
"Programs are poems for computers."
08-06-2017, 11:43 PM
Post: #4
 webmasterpdx Senior Member Posts: 541 Joined: Sep 2015
RE: [cas] use of functions hyperbolic secant and cosecant and inverses
While I have no problem in changing the format of answers, I'm not really fond of basing functionality of the calculator on locale of exams. I'm really tired of basing the functionality of the prime on the lowest common denominator. I'm an engineer and I also do some math research, and I want to use my calculator at that level. To put it another way.....how would you feel if it were changed to output everything in terms of grade school level math....I mean that's kinda ridiculous.
08-07-2017, 11:12 AM
Post: #5
 matthiaspaul Senior Member Posts: 385 Joined: Jan 2015
RE: [cas] use of functions hyperbolic secant and cosecant and inverses
(08-06-2017 11:43 PM)webmasterpdx Wrote:  While I have no problem in changing the format of answers, I'm not really fond of basing functionality of the calculator on locale of exams.
I was not suggesting to not implement them (the opposite is true), but was trying to think of reasons why they didn't implement them already (and suggested possible ways to overcome potential issues).
In fact, the system should accept all functions on input, it should just avoid output in terms of "suppressed" functions. By default, all functions should be in the "not suppressed" state, of course.

Greetings,

Matthias

--
"Programs are poems for computers."
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