I just wanted to point out you may be confused on how toggleClass works. The second parameter is never a string like a class. Instead, it's a boolean. I've gotten rid of the "shown" class (things are shown by default) and used a boolean for the second argument:
i=0;
$('#mybutton').click(function(){
i++;
$('#euro').toggleClass('hidden', i%3!==0),
$('#pound').toggleClass('hidden',i%3!==1);
$('#dollar').toggleClass('hidden',i%3!==2);
});
All this does is remove the hidden class when the cycling matches (i%3===0) and add it (hide those elements) otherwise.
If you did want to toggle between multiple classes, I believe the first argument should be a space separated list of classes.