From what I can see the 11C is powerful enough to do much of what you want and even be programmed to do so. There are libraries of programs and solutions books for many similar calculators from the HP-34C the HP-65 and 67, HP-25 and so forth that have the ABCDE keys.
Since you know the math, you may need to lean the calculator, how to use RPN and some simple programming should follow along. Usually all these calculators came with a good instruction manual that will contain essentially a tutorial on problem solviing using the calculator manually. Then existing programs can serve as a learning tool, or be adapted to the 11c, specifically for the traverse and inverse functions. Much can be accomplished from the keyboard with the basic trig functions, pi, and a page of curve formula's. Traversing and inversing can also be done without a program by mastering the polar to rectangular functions and judicious use of a few storage registers.
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