Trig Func Plot Error and Trig Solving Error

[Bosebcc]

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.