Solving a = sin(c)cosh(d) and b = cos(c)sinh(d) for c and d

[ChrisHarvey]

Can anyone analytically solve these 2 simultaneous equations for c & d, where a and b are known?

a = sin(c) * cosh(d)
b = cos(c) * sinh(d)

I can eliminate 'c' to get:

(sinh d)^2 = b^2 + (a^2)*(tanh d)^2

but this doesn't seem to make life any easier.

 

[ChrisHarvey]

Arggghhhh... I've just this second seen how to do it: write (tanh d)^2 as 1/(cosh d)^2 and then (cosh d)^2 as 1 + (sinh d)^2, multiply though by (sinh d)^2, and solve as a quadratic.

I have an annoying habit of asking for help and then doing it myself a few minutes later... sorry.