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Trig Func Plot Error and Trig Solving Error
10-27-2019, 08:38 AM (This post was last modified: 10-30-2019 10:08 AM by Bosebcc.)
Post: #1
Trig Func Plot Error and Trig Solving Error
I have encountered 3 problems regarding plotting and 2 problems regarding solving fcn.

There are 2 sources that should display the correct graph and answer I will reference: Wolfram, Desmos

Please refer to the number(ex:[1]) to answer any question so we can be clear and topic number (ex:#1) for reference.


#1 Graphing Certain Function will also graph the asymptote (Note: this only happend in the Advance graphing)

HP Prime: (Advance Graphing)
Ref: (Desmos)
As you can see there shouldn't be 2 vertical line where the asymptote are.

[1] Why is there a asymptote for some graph and not for others? (The reason I want the advance graphing app to work properly is because of the numerical feature where you can choose any Point of Interest and it will show all the x values and y values. This will be related to 2 other questions in this thread [2],[3] )

#2 Whenever I want to find intersections for two equation and list it out in the numerical view. Sometimes the Hp Prime will just calculate the value forever and doesn't continue to display the next value. (cot(x)^2 + 3*csc(x) = 3)

Ref: (Advance Graphing Symbol) (Advance Graphing Numerical) (Advance Graphing Plot)

[2] Is there a way to limit the computation time or skip the value the numerical view is trying to calculate when I am satisfy with the approximation. (You may ask why do you want to view the intersection when you can just solve or fsolve in the cas mode, please refer to #3)
Ref: Advance Graphing App Numerical View (Tracing intersection of function y=cot(x)^2 + 3*csc(x) & y=3)

#3 Solve and fsolve doesn't display all the values. (cot(x)^2 + 3*csc(x) = 3)
-Normally I would just input the equation into the solve() with no argument at all.
HP Prime vs Wolfram
HP Prime doesn't show any interval (Ex: 2*pi*n - ...) which mean I can't figure out how many values of x will satisfy the equation in a certain interval range.

-Because of this I resorted into using solve(cot(x)^2 + 3*csc(x) = 3,x,0..2pi) to manually specify the interval and let it display all the values. The problem is it doesn't.
HP Prime vs Wolfram
You can see the Hp prime is missing one solution.(Note this also happen if I use fsolve(cot(x)^2 + 3*csc(x) = 3,x,0..2pi)

This is why I want to use the advance graphing app as a double check, but nothing is working.

- Even though using solve(cot(x)^2 + 3*csc(x) = 3,x,0..2pi) doesn't display the 1.57 solution, I can give it a guess using solve(cot(x)^2 + 3*csc(x) = 3,x,1.5) and it will display the missing solution.
HP Prime

[3] This is very frustrating because it doesn't show all the solution and this led me into thinking that my own work is wrong. The question is what did I do wrong or is this a bug.


#4 Certain graphs are completely wrong when plot.
Ex (Fcn) : HP Prime(Normal Graphing) vs HP Prime(Advance Graphing) vs Wolfram

[4] Can anyone explain the different in algorithm behind the advance graphing app and the normal graphing app
[5] Why can't the advance graphing app display a correct graph for many fcns.

#5 My HP Prime seems to crash very often in the middle of a calculation. [6]
I heard this is a common thing, but is there a way to at least partially fix this problem.
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10-28-2019, 07:53 AM
Post: #2
RE: Trig Func Plot Error and Trig Solving Error
Quote:[1] Why is there a asymptote for some graph and not for others?
Well, even the internal representation of the relation
Y=1/(X-1)+2/(X-1)
in the Advanced Graph App on my Android Emu decides to draw a vertical line on the definition gap X=1. But no line at X=1 for
Y=1/(X-1)+1/(X-1)
!?? Strange.
But maybe an acceptable workaround could be drawing the result of the CAS command collect of the function? So in your case:
collect(cot(x)^2+3*csc(x))
The result
(1+3*sin(X)-sin(X)^2)/sin(X)^2
has no assymtote anymore.
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10-28-2019, 05:59 PM
Post: #3
RE: Trig Func Plot Error and Trig Solving Error
My 2 cents...

Here is my comprehension of what a graphing app is : it does not analyse the formulas it has to draw, it draws them, avoiding errors such as division by zero or impossible values (log of negative numbers, ...).

When drawing, the Advanced Graphing seems to use iterations to refine the graphics, but also - maybe - lines between points. And this leads to the vertical bars, that you know should not exist. They also appear on your good old HP48G, eg when you graph TAN(X).
   

I’m not sure I would have used Advance Graphing to analyze a function (x->f(x)), because there is an app for this : Function.
To my comprehension, Advanced Graphing is advanced in the fact that it can handles other graphical drawing than just functions : inequalities, formulas composed by combinations of X and Y (and not only Y=f(X)).
But to study a function, the app Function is not so bad. And it draws your formula very well Smile

What I would have done :
Draw the function with Function.
Find the intersection with Y=3 with Function (Menu, Fvn, Intersection), and also find the extrema, …
   

Analyze the domain of the function using CAS (domain()).
Find the extrema using CAS (zeros(f’(x))), also find the intersections with g(x)=3, ...
   

I let you recompose my experimental answer in terms of #1, #2, [1], [2] and [3].
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10-29-2019, 02:22 PM
Post: #4
RE: Trig Func Plot Error and Trig Solving Error
(10-28-2019 05:59 PM)pinkman Wrote:  My 2 cents...

Here is my comprehension of what a graphing app is : it does not analyse the formulas it has to draw, it draws them, avoiding errors such as division by zero or impossible values (log of negative numbers, ...).

When drawing, the Advanced Graphing seems to use iterations to refine the graphics, but also - maybe - lines between points. And this leads to the vertical bars, that you know should not exist. They also appear on your good old HP48G, eg when you graph TAN(X).


I’m not sure I would have used Advance Graphing to analyze a function (x->f(x)), because there is an app for this : Function.
To my comprehension, Advanced Graphing is advanced in the fact that it can handles other graphical drawing than just functions : inequalities, formulas composed by combinations of X and Y (and not only Y=f(X)).
But to study a function, the app Function is not so bad. And it draws your formula very well Smile

What I would have done :
Draw the function with Function.
Find the intersection with Y=3 with Function (Menu, Fvn, Intersection), and also find the extrema, …


Analyze the domain of the function using CAS (domain()).
Find the extrema using CAS (zeros(f’(x))), also find the intersections with g(x)=3, ...


I let you recompose my experimental answer in terms of #1, #2, [1], [2] and [3].

Thank you for the reply. I appreciate the help. There was one limit which kept me from using the function app you have mention. It can only show one POI(Function (Menu, Fvn, Intersection) at a time. Which I will explain in [3].

As you may have noticed the original thread missed some of the question and one of those is why I use advance graphing app. (I'm a new user and the forum didn't allow me to attach multiple links.)

-Here is the rest of the post (I will try and edit the original post if possible)-

#3 Solve and fsolve doesn't display all the values. (cot(x)^2 + 3*csc(x) = 3)
-Normally I would just input the equation into the solve() with no argument at all.
HP Prime vs Wolfram
HP Prime doesn't show any interval (Ex: 2*pi*n - ...) which mean I can't figure out how many values of x will satisfy the equation in a certain interval range.

-Because of this I resorted into using solve(cot(x)^2 + 3*csc(x) = 3,x,0..2pi) to manually specify the interval and let it display all the values. The problem is it doesn't.
HP Prime vs Wolfram
You can see the Hp prime is missing one solution.(Note this also happen if I use fsolve(cot(x)^2 + 3*csc(x) = 3,x,0..2pi)

This is why I want to use the advance graphing app as a double check, but nothing is working.

- Even though using solve(cot(x)^2 + 3*csc(x) = 3,x,0..2pi) doesn't display the 1.57 solution, I can give it a guess using solve(cot(x)^2 + 3*csc(x) = 3,x,1.5) and it will display the missing solution.
HP Prime

[3] This is very frustrating because it doesn't show all the solution and this led me into thinking that my own work is wrong. The question is what did I do wrong or is this a bug.


#4 Certain graphs are completely wrong when plot.
Ex (Fcn) : HP Prime(Normal Graphing) vs HP Prime(Advance Graphing) vs Wolfram

[4] Can anyone explain the different in algorithm behind the advance graphing app and the normal graphing app
[5] Why can't the advance graphing app display a correct graph for many fcns.
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10-29-2019, 06:13 PM (This post was last modified: 10-29-2019 06:33 PM by Tim Wessman.)
Post: #5
RE: Trig Func Plot Error and Trig Solving Error
(10-29-2019 02:22 PM)Bosebcc Wrote:  - Even though using solve(cot(x)^2 + 3*csc(x) = 3,x,0..2pi) doesn't display the 1.57 solution,

Erm? What is the 1/2*pi you are showing?


Also, for that plot you show, try checking the "allow complex output from real input" in page 1 of Home settings.

Quote:[5] Why can't the advance graphing app display a correct graph for many fcns.

Such as?

TW

Although I work for the HP calculator group, the views and opinions I post here are my own.
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10-29-2019, 09:12 PM (This post was last modified: 10-29-2019 10:45 PM by pinkman.)
Post: #6
RE: Trig Func Plot Error and Trig Solving Error
Bosebcc, I really like your problems.
How did you find these expressions that push our calculators to their limits?!

I think Wolfram alpha is a bit straightforward, as CAS and the Prime let (force) you chose the parameters and conditions of the question.
Try to analyze the domain of your f(x)=abs(sin(x)/...) function (with CAS or Wolfram alpha), and you’ll see it is not as trivial as Wolfram alpha seems to affirm when plotting the function.
Also, analyze the domain of x^x and you’ll confirm that Wolfram alpha gave you a solution without letting you chose your definition of negative power of negative numbers.

Once again, for me, the Advanced Graphing app doesn’t appear to be the best solution to analyze a function, even to double check as you said.
But I would like to hear people stronger than me in mathematics, or, as you asked, knowing the way it draws, before concluding the shown graphic is wrong.

Like Tim I also don’t understand why you say x=pi/2 is not an intersection of your previous f(x) with g(x)=3, because CAS found it : [1/2*π,-asin(1/4),asin(1/4)-π]

Regards.
Thibault
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10-30-2019, 02:20 AM
Post: #7
RE: Trig Func Plot Error and Trig Solving Error
Oh, I forgot to mention - if you want the general periodic solutions like 2*n, uncheck the ""principal solutions" check on page 1 of the CAS settings page. I think that does what you are looking for.

As to why the "allow complex result from real input" checkmark makes a difference here, you have (-X)^(-X)|X<0 power which does not have a non complex result. Since many teachers want negative exponents to "error" until they are ready to teach about it, this is the default setting.

Smile

TW

Although I work for the HP calculator group, the views and opinions I post here are my own.
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10-30-2019, 09:57 AM
Post: #8
RE: Trig Func Plot Error and Trig Solving Error
(10-29-2019 06:13 PM)Tim Wessman Wrote:  
(10-29-2019 02:22 PM)Bosebcc Wrote:  - Even though using solve(cot(x)^2 + 3*csc(x) = 3,x,0..2pi) doesn't display the 1.57 solution,

Erm? What is the 1/2*pi you are showing?


Also, for that plot you show, try checking the "allow complex output from real input" in page 1 of Home settings.

Quote:[5] Why can't the advance graphing app display a correct graph for many fcns.

Such as?

Thank for your reply it have been very helpful. First of all checking "allow complex output from real input" did the job for the graph in the function app. I am still confuse why the advance graphing app show two line. Maybe it's a limitation of the graphing engine(http://www.peda.com/grafeq/) or I have some setting on which cause the result.

(10-29-2019 09:12 PM)pinkman Wrote:  Like Tim I also don’t understand why you say x=pi/2 is not an intersection of your previous f(x) with g(x)=3, because CAS found it : [1/2*π,-asin(1/4),asin(1/4)-π]

Regards.
Thibault

//1 For the pi/2 result, I do understand see that that is the solution. But it still doesn't explain why fsolve or solve can't show all the solution in the interval. I'm sorry that I didn't provide a clear example that indicate the problem. For example the interval 2pi..4pi for the same function. In the hp prime using solve(cot(x)^2 + 3*csc(x) = 3,x,2pi..4pi) It returns 9.677, 12.313 instead of 7.854, 9.677, 12.313

_______________________________________________________________________

_______________________________________________________________________

(10-30-2019 02:20 AM)Tim Wessman Wrote:  Oh, I forgot to mention - if you want the general periodic solutions like 2*n, uncheck the ""principal solutions" check on page 1 of the CAS settings page. I think that does what you are looking for.

As to why the "allow complex result from real input" checkmark makes a difference here, you have (-X)^(-X)|X<0 power which does not have a non complex result. Since many teachers want negative exponents to "error" until they are ready to teach about it, this is the default setting.

Smile

//2 Thank you for this too. I have one question about the output of principal solution. In the result of the periodic solution, it includes n_2,n_3,n_3. I have not seen this notation before. Is this the notation for interger and is n_2 the same as n_3?

________________________________________________________________________________​______________________________________________________________
(10-28-2019 07:53 AM)FrankP Wrote:  
Quote:[1] Why is there a asymptote for some graph and not for others?
Well, even the internal representation of the relation
Y=1/(X-1)+2/(X-1)
in the Advanced Graph App on my Android Emu decides to draw a vertical line on the definition gap X=1. But no line at X=1 for
Y=1/(X-1)+1/(X-1)
!?? Strange.
But maybe an acceptable workaround could be drawing the result of the CAS command collect of the function? So in your case:
collect(cot(x)^2+3*csc(x))
The result
(1+3*sin(X)-sin(X)^2)/sin(X)^2
has no assymtote anymore.

//3 That solves the problem for this function but there is another problem. Yesterday I found a function while doing a problem that had the same issue(asymptote appearing)
and I tried to use the collect function but this time the asymptote didn't go away. [I can't find the function, I will try to find it and post an update]
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10-30-2019, 10:03 AM (This post was last modified: 10-30-2019 10:04 AM by Bosebcc.)
Post: #9
RE: Trig Func Plot Error and Trig Solving Error
(10-29-2019 09:12 PM)pinkman Wrote:  Bosebcc, I really like your problems.
How did you find these expressions that push our calculators to their limits?!

I think Wolfram alpha is a bit straightforward, as CAS and the Prime let (force) you chose the parameters and conditions of the question.
Try to analyze the domain of your f(x)=abs(sin(x)/...) function (with CAS or Wolfram alpha), and you’ll see it is not as trivial as Wolfram alpha seems to affirm when plotting the function.
Also, analyze the domain of x^x and you’ll confirm that Wolfram alpha gave you a solution without letting you chose your definition of negative power of negative numbers.

Once again, for me, the Advanced Graphing app doesn’t appear to be the best solution to analyze a function, even to double check as you said.
But I would like to hear people stronger than me in mathematics, or, as you asked, knowing the way it draws, before concluding the shown graphic is wrong.

Like Tim I also don’t understand why you say x=pi/2 is not an intersection of your previous f(x) with g(x)=3, because CAS found it : [1/2*π,-asin(1/4),asin(1/4)-π]

Regards.
Thibault

I found these problems while checking my homework XD. I don't necessary like to use the Advance graphing app to analyze a function. But because you can't list out the POI in the function app numerical view which the Advance graphing app numerical view can, and I still can't get a decent answer from the cas view. I still rely on this app to work properly.

Sincerely
Bosebcc
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