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Roger
Further to my previous post.  When looking at formula involving trig functions in textbooks, I find carrying on into the worked examples of great value in getting a feel for what’s really going on.  Similarly, after putting a formula together involving just symbols, I find it essential to test it using simple real values which you can almost do in your head, e.g. 360, 030, 060, 090 degrees.  It’s amazing how many mistakes you’ll pick up.  This morning’s “I’ll soon knock this off in a couple of minutes” turned into half an hour’s ‘Brain Trainer’.  E.g. with only distance gone and course, you can’t find mid-lat without knowing your northings, which means you need to calculate northings as well as eastings. 

A few checks to keep in the back of your mind: Between 360- and 090-degrees northings will gradually reduce from distance gone to zero, and eastings will gradually increase from zero to distance gone.  Unless you’re at the equator, ch-long is always more than eastings.  At 60N or S, it’s twice eastings.  As you approach the Poles ch-lat gets many times more than eastings, and until the arrival of GNSS and their associated receiver software you’d have had to use ‘grid’ navigation.  DaveP