acos (arc cosine, i.e., inverse of
cosine) 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(45)}
3.141592653589793
% tcl::mathfunc::acos {45}
expected floatingpoint number but got "45"
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