What are some real life situations that may be modeled by a sine or cosine curve?
Sine and cosine curves are crucial to the analysis of anything involving oscillation or rotation — sound waves, vibration, radio waves, the beating of your heart, all types of rotary engines, and so on. Even if the sound, vibration or whatever is not a pure sine or cosine wave, a mathematician called Fourier showed that *all* repeating patterns could be constructed as the sum of a load of sine and cosine waves at integer multiples of some “fundamental” frequency. He then went on to show that any waveform — repeating or not — can be constructed as the sum of a load of sine and cosine waves if you drop the requirement that they be integer multiples of some frequency. These two discoveries — Fourier Series and Fourier Transforms, respectively, are hugely important across engineering and the sciences. This message wouldn’t get to you if some engineer had not done some sums with sine and cosine waves to work out how to get the data through my telephone wire!
