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Just for the sight reduction I propose a Gilson Midget Circular Slide Rule.  I was not aware of these until a few days ago and I'm now waiting on delivery of one. They have sine and cosine scales on the back in approximate linear fashion. This avoids the compression at high sine and low cosine values. From photos I read sin 89/cos 1 as 0.9984 and sin 1/cos 89 as 0.016. The trig scales are split into three concentric arcs but don't look like it would take much practice to get used to them. These scales are only used for lookup and the values would have to be recorded and then calculated on the approximate 12" slide rule side. 

This same linear scale idea could be printed on a sheet of paper with comparable accuracy.

I am confident that I can enter .999 with +/-  .002 accuracy. I do not feel confident setting a slide on the trig scale to anywhere close to sine 80.

For a clear picture of the trig scales, look up on eBay "Gibson midget slide rule". Gibson is a spelling error. This older version has the complete scale in one arc.  It's appealing but the seller says the disc is, 100 year old, plastic. Mid 1930's versions have aluminum discs. These are 4" diameter slide rules - thus the Midget part.          Regards, Noell