What is sin?!

One of the toughest things that I've come across when teaching the sine, cosine and tangent ratios has been just explaining what they are. Many students just want to know what they are and they can't accept the time-old argument, "Sin is sin, leave it at that."

First of all, it's hard to explain that it's a ratio and a function, especially when they don't really understand what a function is yet (the order isn't right - we do trig before functions). It's hard for them just to accept that stuff happens to the angle and taaaa-daaaa! we get a new number.

My father suggested that I put up a few iterations of the Maclaurin series for sinx. Just a few and explain how this is how our calculators approximate sinx.  It's something to start off with. I could just give them a small preview, that it is a number that we can approximate. It was a really great idea and I'll keep that in mind.