NavList:

Having not used a slide rule in earnest since my last BSc exam in June 1966, I thought it was about time I got into practise again using the various bits of slide rule I’ve rescued from the bottom drawers of desks I’ve inherited over the years.  Having revised multiplication and division, I looked for trig functions.  First problem, there’re no cosines.  Presumably this is got around from cosine angle = sine 90- angle.  Next problem, the trig functions are on the stock, not the slider.  Is there a way to multiply more than one sine at a time without having a good memory for numbers (like more than two seconds) or writing the value down?

One rather upmarket Government 10” slide rule, with a spare cursor and a tightening key, that I’ve rescued appears to have a way around this.  The trig functions are on the rear of the slider.  If you’ve got more trig functions than numbers, you can turn the slide upside down and use that side. The only problem is working out where left-hand one is.  Right hand one’s OK; its sine 90.

Using Greg’s example, I was getting answers in the region of 1.7-1.8, but by golly you need good eyesight.  I wouldn’t like to try it in a bumpy boat or aeroplane on a dark night.  Using a x10 magnifier, I managed to get 1.775. 
I didn't pursue the calculator solution, but presumably you need to spend time converting from degrees and minutes to decimals of a degree. DaveP