Mercator Sailing: Course and Distance

[Albert Chan]

(08-26-2018 07:18 AM)Dieter Wrote:  Hint: the expression ln(tan(45°+x/2)) in the "book" formula is equivalent to artanh(sin(x)).

FYI, atanh(sin(x)) = asinh(tan(x)) = gd^-1(x) = x + x^3/6 + x^5/24 + ...

https://en.wikipedia.org/wiki/Gudermannian_function
The Secret Connection between Hyperbolic and Trigonometric Functions