A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Robert Bernecky
Date: 2015 May 17, 07:01 -0700
I would write it as "haversine of angle 45° has the numerical value 0.1464466"
to calculate hav(x) you can use either
the latter expression means first halve the angle e.g. 45/2 = 22.5 deg. , then find the sin(22.5°) = 0.3826834
finally square this to get 0.1464466 which matches what you get using the first expression (1- cos x)/2
You will also want to know how to find the "inverse haversine": given that haversine of some angle is 0.1464466 , what angle is that?
as Frank Reed posted, you can find x using
cos x= 1- 2*0.1464466
cos x = 0.707106781
now use a calculator to find the inverse cosine of 0.707106781
x = cos-1 (0.70710678) = 45°