In Danish, "my" & "mine" is either min, mit, or mine, the differences are:
min = when the following word uses -en : The dog is eating my food = Hunden spiser min mad. (mad is an -en word, as you'd say maden for 'the food')
mit = when the thing that's owned is a -et word : You are eating my apple = Du spiser mit aeble (mit is an -et word, as you'd say aeblet for 'the apple')
mine = when there is a plural of the thing being owned : I have my horses = Jeg har mine heste (But if you were saying "I have my horse" - just the one horse- it would be "Jeg har min hest")
"Sin" is for singular -n words, and "Sit" is for singular -t words:
"De spiser sin ost" = They eat their (own) cheese.
"Hun spiser sit brød" = She eats her (own) bread.
"Sine" is for both -n and -t plural words:
"Han spiser sine appelsiner" - He eats his (own) oranges.
"Katten spiser sine æbler" - The cat eats his (own) apples.