Question: Sinc() Function

It's disappointing that after all these years, Maple still hasn't implemented a real sinc() function, in which an expression with a trig expression(s) can be entered as an argument, with a return value that is expressed as a sinc() function(s), not a return of sin() functions, which is what I get when I try to define my own sinc() function. I find that the Sinc function in the Dynamic Systems package to not be very useful for general Maple calculations.

The following code converts an expression containing a trig function to a sinc-function expression. How can this code (or some other code) be implemented in Maple by defining a real sinc function that accepts an expression in its argument and returns an evaluated sinc function, not a return value that has sin functions?

eval(expr, {sin = (x -> x*sinc(x)), 
              cos = (x -> (x+Pi/2)*sinc(x+Pi/2)),
              tan = (x -> x*sinc(x)/(x+Pi/2)/sinc(x+Pi/2))});

Attribute: This code was originally posted by  Robert Israel 6577

Thanks for any assistance.