How to apply a constant function to a vector of values?

I have a list of functions

func[x_]={1,Cos[x],Sin[x]}

(for example) and I want to apply each function to a list of values

xval={a,b,c,d}

obtaining a list of tuples. The problem is that the constant function will not evaluate to a tuple (it will remain as a scalar)

func[xval] = {1, {0, -1, 0, 1}, {1, 0, -1, 0}}

Is there a way to force the creation of a tuple (with the function value) of the same size as xval, if I don't know what are the functions in func (if there is or not a constant function in it)?

Answer

The reason why it works with Cos and Sin is that those functions are Listable. So just make a constant function that is Listable, too:

func[x_]:={Function[y, 1, Listable][x],Cos[x],Sin[x]}
xval={a, b, c, d}
func[xval]

(*
==> {{1, 1, 1, 1}, {Cos[a], Cos[b], Cos[c], Cos[d]},
     {Sin[a], Sin[b], Sin[c], Sin[d]}}
*)

Note that here it is important that you use := to define func, otherwise it gets evaluated already at definition time, resulting in a single 1 again.

If you need it often, you can define a function to generate a listable constant function:

const[x_] := Function[y, x, Listable]

Then you can write:

func2[x_] := { const[1][x], Cos[x], Sin[x] }
func2[xval]
(*
==> {{1, 1, 1, 1}, {Cos[a], Cos[b], Cos[c], Cos[d]}, 
     {Sin[a], Sin[b], Sin[c], Sin[d]}}
*)