Simplified Lucas angles for hyperbolic functions

Working with banker bot led me to develop a simple scheme to generate Lucas based Sinh and Cosh. They are actually additive if you look closely. There is also a simple 2 by 2 symmetric matrix of (phi + 1/phi)/2 and (phi - 1/phi)/2 that generates one pair from the previous pair.  These are thus additive, include both sinh and cosh and so can be the equilibrium functions for keeping loans and deposits stable in the banking chain.

cosh(2) = cosh(0) + sinh(1)
sinh(3) = cosh(1) + sinh(2)

 

Lucas Index	Sinh	Cosh
0	0.0000	1.0000
1	0.5000	1.1180
2	1.1180	1.5000
3	2.0000	2.2361
4	3.3541	3.5000
5	5.5000	5.5902
6	8.9443	9.0000
7	14.5000	14.5344
8	23.4787	23.5000
9	38.0000	38.0132
10	61.4919	61.5000
11	99.5000	99.5050
12	160.9969	161.0000
13	260.5000	260.5019
14	421.4988	421.5000
15	682.0000	682.0007
16	1103.4995	1103.5000