Definitely pathos. You are trying to appeal to her emotions. Logos is no because there is no logic in eating a cookie on a strict diet. Ethos is no because you are not trying to appear credible by asking her to eat the cookie
You'll hate past you for not putting in the extra effort over the summer, and having a head start on your work will really help you out. then you will have less stressed filled nights and spend more time enoying the little bit of free time you get.
