We all know that it’s more than polite to cover your mouth when you cough; it makes good public health sense. Oh, I can still hear my mother’s voice ringing in my ears. I can hear my own voice ringing in my daughters’ ears, for that matter.
But, you should cough into the crook of your elbow or your shoulder rather than into your hands. That way if you are contagious (and it is really hard to know if you aren't), the germs coming out of your mouth don’t make it onto your hands. Since you are less likely to touch things with your elbow or your shoulder, the germs won’t spread.
So do like your mother told you and cover your mouth when you cough -- just do it with your elbow.