Permalink Submitted by Anonymous on February 25, 2014

Napier and Regiomontanus before him knew the formulae for constructing sine and cosine tables. Basically this is sin2u equals 2sinu.cosu. This can be converted into sin2u equals 2sinu. (1-[sinu]^2)^0.5 ,so that if the sine of a particular angle is known then the cosine can be calculated, also the sine of half that angle can be calculated by quadratic equation. The sine of 75 degrees can therefore be calculated from bisecting sin30 degrees ( which is 1/2) to give the sine of 15 degrees which is the cosine of 75 degrees, from which the sine of 75 degrees can be calculated. submitted by Peter L. Griffiths.

## Napier's logarithms

Napier and Regiomontanus before him knew the formulae for constructing sine and cosine tables. Basically this is sin2u equals 2sinu.cosu. This can be converted into sin2u equals 2sinu. (1-[sinu]^2)^0.5 ,so that if the sine of a particular angle is known then the cosine can be calculated, also the sine of half that angle can be calculated by quadratic equation. The sine of 75 degrees can therefore be calculated from bisecting sin30 degrees ( which is 1/2) to give the sine of 15 degrees which is the cosine of 75 degrees, from which the sine of 75 degrees can be calculated. submitted by Peter L. Griffiths.