acos (arc cosine, i.e., inverse of [cos]ine) is one of the math commands available in [expr], as well
as in the tcl::mathfunc:: [namespace] as of Tcl 8.5.

    :   '''[expr]''' { '''acos'''(''expression'') }
    :   '''[tcl::mathfunc]::acos''' ''numericValue''

It is a procedure which provides command access to the [expr] math function, taking the same arguments as the expr function and taking expressions as arguments as well.

[LV] 2007 Oct 31

Is the following one of the differences between using acos in expr and as a
command? The above comment says "taking the same arguments as the expr function 
and taking expressions as arguments as well" - is there something special
needed for the expressions to the procedure?
======
$ tclsh8.5
% expr {acos(4-5)}
3.141592653589793
% tcl::mathfunc::acos {4-5}
expected floating-point number but got "4-5"
======

[DKF]: That's just the difference between expressions and commands.
----

One good use for [acos] is to get the constant Pi:

======
% expr acos(-1)
3.141592653589793
% tcl::mathfunc::acos -1    ;# In Tcl 8.5
3.141592653589793
======

<<categories>> Command | Function | Mathematics | Syntax