The sine function

A pupil was having difficulty with the concept of a sine. What is a sine? Why should the ratio of the length of the line in a triangle opposite an angle, to the length of the line adjacent to the angle matter? Why would anyone bother with it? What was the point? Because of the use of the electronic calculator, to this pupil a sine was just a magical number that appeared when he pressed a button… he was perplexed, where did the calculator get it from? When I learnt about the sine function at school, I was given a book of mathematical tables. When I looked for the sine of an angle I could see what the numbers for other angles were. I got a feeling for the relative values of the function for various sizes of angle. I learnt by observation that the sine function varied from –1 to 1. I realised that calculating the sine function itself was difficult to achieve… that’s why I was using a table containing pre-calculated values to look up the value I needed. But none of these observations are available to the modern pupil, just the magic calculator button.
I explained the sine function as the distance that a shaft connected to rotating wheel moves vertically and that the cosine is the distance that the shaft moves horizontally. As soon as I’d done that, the pupil saw the reason for the function, that it was about knowing where the piston on an engine was relative to the position of the crankshaft, or how the various levers on a loom move as the driving wheel move around. At Puppet Maths we relate maths functions to the real world, so that they become relevant to the pupils.