I have a student who is looking at the history of trigonometry. My question is,
"When did someone decide to look at the sine of an angle greater than 90 degrees?"
It doesn't make much sense to talk about a chord of an arc greater than a semicircle so half-chords seem to be limited to under 90 degrees. I can trace the notion of the sine as a circular function to the work on the cycloid in 1600's. Is there any occurance before this?