Trig Func Plot Error and Trig Solving Error

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(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

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.