We all know that it’s more than polite to cover our mouths when we 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 because I must say the phrase 20 times a day.
Regarding public health, you should really aim your cough into the crook of your elbow or your shoulder, and away from 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, which interact with the world by touching. Since you are less likely to touch things with your elbow or shoulder, the germs won’t spread. This isn't just for coughing. I have heard the catchy phrase "Sneeze into your sleeve" lately, too!
So do like your mother told you and cover your mouth when you cough — just do it with your elbow.