Dr. Pepper-
Thanks for the hints.
I already realize that only angles 0 – 90 need to be factored, because 91 – 180, 181-270 and 271 – 360 just duplicate the coverage the pencil achieves with 0 – 90.
B”N I’ll give it some thought.
(I hope you’re still active in teaching and/or tutoring in some capacity – you have a real talent not only for math but also for making it interesting and conveying the required knowledge and methodology.)
Oh, here’s something that maybe you can use: ??
If it didn’t come out well, it’s because I never tried it before – you can call it my beta theta <gong>.
(cut-and-pasted straight from Wikipedia)