Apply a list of functions on an element

Questions
1

I want to find a quick way to create the expression

{Cos[a],Sin[a]}

instead of typing it explicitly.

What I use now is

({Cos[#], Sin[#]} & /@ {a})[[1]]

Is there any shorter way to do it?

I don’t see any reason for the a to be part of a list.

2

Another form would be:

#[a] & /@ {Cos, Sin}

(* {Cos[a], Sin[a]} *)

What you’re looking for is probably the following:

Through[{Cos, Sin}[a]]

(* {Cos[a], Sin[a]} *)

You can accomplish the above, by the way, with AngleVector[a].

Note that there are some other shorthand forms for these kind of things, at least MinMax, ReIm and AbsArg.

3

Thanks very much!
This is very helpful

4

You can try

AngleVector[a]