How do you end a business e-mail to someone you've never met?

I'm writing a professor to about getting a course p to take her cl or a waiver to skip it because it's a cl I've more or less already taken at another school that transferred in wrong. Being that I attend a very small school, it's common knowledge that this professor is having a difficult time going through a divorce and she's taking it out on the students...so I kind of need to write my e-mail in a fashion that doesn't piss her off even more...especially because she is one of only two professors teaching courses in my major. What is a good farewell? "Sincerely" seems to formal, and "Thank you for your time" seems to blatantly kiss a$$. What is a happy medium?