Preposition "To" to denote the cause of emotion
① I was surprised to know the news.
② I'm sorry to be late.
③ It's good to see you.
I've ever read the "to"s used in sentences like these denote the cause of emotion, you know, why surprised, why feeling sorry, and why feeling good. But as a learner of English, I do not understand the nuance or logic to use "to" to refer to a kind of past event (=cause), even though "to" usually has future image. I'd appreciate if you could fix my somehow wrong impression.