I can see how. In fact I had the same reaction initially (and my parents are graduates, but they don't know the first thing about maths, so they were no help to me either).
I have no idea why I wrote the program to plot a circle that made it obvious what sin and cos were.
In fact I think I might have misremembered my own story. I had a ZX81 first, and I don't think that had a circle function, so it may be that the ZX81 manual explained how you could use SIN and COS to do that.
But I think we can agree that google and wikipedia are wonderful things. The upcoming generations of programmers and mathematicians are going to be Gods. How could they not be with a library like that!