I had missed the first week or so of school in high school because of illness or something I don't remember. It doesn't matter for this conversation. The result is they were doing something called trigonometry and I felt like the others had some context that I didn't.
What exactly is a sine again? Why do I care about the ratio of the sides of a triangle?
The teacher drew a graph of a sine curve on the chalk board. The first question I asked was why did we connect the two points with a line? Just because we know the value of sine zero and sine 30 doesn't mean we can somehow assume we know what sine 12 should do. It could go to infinity. We just don't know at this point. Or the next question, why is it a smooth curved line and not a straight line between zero and ninety?