What are sin and cos and why are they used so frequently in math?
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When you mark a point on a wheel and spin that wheel, the sine tracks the movement of that point in the up-and-down direction (if you plot the sine versus the angle, it makes the characteristic “sine wave” graph). The cosine tracks the movement in the left-right direction, which gives the same “sine wave” graph, just one quarter of a turn ahead.
The reason they are used so frequently is a) that a lot of natural processes tend to produce sine waves, and b) that the rate of change (or “derivative”) of the sine is the cosine, which is the same shape, just shifted by one quarter turn. This gives some neat mathematical properties, which means that mathematicians like to describe all kinds of waves as the sum of different sine waves.
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