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Robin wrote

In an effort to chase away some of the mental cobwebs from the lockdown I tried to work out what these tables were actually doing. In case anyone is interested here's what I came up with,

Thanks. I had guessed that Smart and Shearme had manipulated the sin formula but did not know how they did it. Many decades ago I enjoyed manipulating trig and integral calcul;us expressions but that ability has long gone.  To be honest I do not understand what you have done (-;

I will add a link to this message on the worksheet.