1.Draw a right triangle on a sphere and label the sides and where is the hypotenuse. Let A be the angle opposite side , B the angle opposite side , and C the right angle opposite the hypotenuse .
2.Then Napier’s Formula has two rules: The sine of a part is equal to the product of the tangents of the two adjacent parts. The sine of a part is equal to the product of the cosines of the two opposite parts.
3.In any triangle ABC,
(i)
(ii)
(iii)
4.Considering , whose non-adjacent parts are 𝑎
and 𝑏.By rule (b), cos c = sin 𝑎sin 𝑏, i.e.,cos c = cos a cos b.This becomes obvious from the cosine rule (1), since γ = 90° and, thus, sin a sin b cos γ = 0. In the same way rule (a) for the adjacent parts α and β of c reads
cos c = cot α cot β.
Comments