"His sister is vegetarian."
Translation:Hans søster er vegetar.
"sin" is kind of like a reflexive possessive pronoun, which is used for singular, third person things like "Han spiser sit æble". If you wrote "Han spiser hans æble", it would sound like he's eating another man or boy's apple and would need to be used in context. Here it can only ever be "hans" because it is part of the subject (the first noun in Danish)
See, I am in grade school so I have not yet learned the possesive pronouns and things like that YET, but I see them in my lessons plan in my homeschooling book. What I DO know is that I have gotten these correct so far. How i see it is the word Sin differs with what the subject is. If the subject is she, Sin= her. If the subject is a cat, sin=it's. As far as i have seen, Sin cannot start a sentence so you always know what to type. Do not know if this is all correct, it is just what I have observed and gone by for a while.