Trig Func Plot Error and Trig Solving Error

[pinkman]

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].