It is a trigonometric equation for a right triangle, to find a non-right-angle angle. Using SOHCAHTOA, it is the opposite side divided by the adjacent angle
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A Texas Instruments graphing calculator can be used as a basic calculator, a scientific calculator and a graphing calculator.
No.
Usually a graphing calculator should have all the capabilities you expect from a scientific calculator (and more, since it does the graphing). For more details, check the manual of your calculator if you already have one.
You can calculate this on any scientific calculator. Those calculators don't usually have a special key for the cotangens, but this is the same as 1 / tan(68).
A graphing calculator is a scientific calculator with a graphing display window. Otherwise, there are no limits to the type of calculations that can be made on either of them.