Learning How to Use the Prime G2 - Hallway Pole Problem - In Three Parts

[jlind]

Note:
There’s a limit to the number of images allowed in a posting. I’ve had to break this up into three parts to cope with that . . .
This is Part II of III

Method 3:
This uses the Prime's CAS and calculus functions to solve the problem. Going back to the Function applications Symbolic View I'm making use of the equation entered before as the starting point. Going to the Function application's CAS View (using the CAS button), the function can be called by its variable name "F1(X)" in the calculator that was assigned when it was entered into the Symbolic View. The first task is finding its first differential, aka F'(X), or dF(X)/dX. In the CAS view the function for it is first pulled up using the white Toolbox button. This isn't intuitively obvious. Under the CAS tab I'm going to use "Calculus" which is number 2 on the menu. That will bring up a sub-menu on which I'm going to use "Differentiate" which is the first option listed.



This puts "diff()" function on the calculation entry line. Inside the parentheses I enter "F1(X)" referring back to the equation entered in the Symbolic View, and the equation's variable I want to differentiate for, "X". It is case sensitive.



Pressing the "Enter" key instantaneously returns the first differential.



Going back to the Symbolic View, F2(X) is highlighted so F'(X) can be entered there. Using the black "Menu" button brings up the option to get an equation from CAS, which is where we left the F'(X) result.



This brings up a window of calculations and results in CAS. The F'(X) differentiation result is highlighted. The highlighting can be moved up and down to get the desired equation. It's the last one calculated, so it's automatically highlighted.



Once pulled in, the equation is on the equation entry line in the Symbolic View.



Highlighting the space for F2(X) and hitting the enter key puts it into F2(X).



To find the root (or zero) of F'(X), I return to the CAS view and use the toolbox again. This time I use the Solve sub-menu. While the "Zero" would be the intuitive choice, it will return more than one zero. I need to specify the 0 to 90 degree domain which the "Zero" function won't allow. For that, I need to use the Numeric Solve, which is number 6 on the Solve sub-menu.



This puts the "fsolve" function on the entry line. F2(X) with the X variable are entered in, and the next option, "0..90", specifies the domain over which it's to be solved, 0 - 90 degrees, which are the outside limits on the angle in this problem.



Hitting the "Enter" key calculates the root as X ~= 38.44 degrees, which is what was found before doing it by hand, and then using the graphing Extremum finder.



To be continued and finished in Part III . . .

John