Add hyperbolic trig functions

[rtavenner]

Suggestion: Provide hyperbolic trig functions (sinh, cosh, tanh, asinh, acosh, atanh) in Basics.
All of these are already javascript functions (Math.cosh, Math.sinh, etc.), so this should be easy to implement.

Current workaround:

cosh : Float -> Float
cosh x = (e^x + e^ -x) / 2
sinh : Float -> Float
sinh x = (e^x - e^ -x) / 2
tanh x : Float -> Float
tanh x = sinh x / cosh x
asinh : Float -> Float
asinh x = logBase e (x + sqrt (1 + x^2))
acosh : Float -> Float
acosh x = logBase e (x + sqrt (x^2 - 1))
atanh : Float -> Float
atanh x = (logBase e ((1 + x) / (1 - x))) / 2

(I got these formulas from Wolfram Mathworld.)

I use these functions a lot! In my own code, I have manually defined cosh and sinh 5 times, acosh 3 times, and asinh twice.

Note: This suggestion probably belongs in the meta-issue "Math and Numbers" (#721).

[evancz]

I believe that adding these to Basics would be a breaking change. In the unlikely event that code like import Something exposing (cosh) is out there, it would be cause an "ambiguous name" error.

Idea to create a Math module could be relevant, so linked for reference. #1088

[JoshuaHall]

What functionality would adding these break? Wouldn't this be a semver minor update, since you are just adding a feature? While adding this feature could potentially make other libraries slightly less useful or cause conflicts/import errors, those errors aren't really your concern because the benefits of adding this outweigh the slight negatives in the short term.

[rtavenner]

This was a surprise. I had completely forgotten I had posted this issue!

I believe that adding these to Basics would be a breaking change. In the unlikely event that code like import Something exposing (cosh) is out there, it would be cause an "ambiguous name" error.

Huh. That didn't occur to me. And it's not even as unlikely as you suggest — that actually appears in my own code.

(The module that exposed cosh was one I had written myself, to work around the fact that these functions weren't builtin.)