What are sin and cos and why are they used so frequently in math?
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Imagine a rider on a carousel. You are looking down on it from above (as if in a helicopter). The rider starts due east of the center point of the carousel, and begins to travel around, making an always changing new angle, measured from the current position, the center of the carousel, and the starting “due east” point.
You are keeping track of how far north the rider is from the center of the carousel, as a percentage. The farthest north they can go is 100% north, and the farthest south they can go is “-100% north”. The sine [of the current angle] measures “northness.”
You are also keeping track of how far east the rider is from the center of the carousel, as a percentage. The farthest east they can go is 100% east, and the farthest west they can go is “-100% east.” The cosine [of the current angle] measures “eastness.”
At any point along the ride, you can describe how much north and east the rider is based solely on the angle.
Usually in math, we prefer “1 and -1” instead of “100% and -100%” but they mean the same thing. That’s why sine and cosine values are usually a decimal like “0.375” instead of “37.5%.”
Anything that moves back-and-forth in one or two dimension (like north and east) follows some variation of the sine/cosine rules of “northness” and “eastness” even if the exact formulas describing their motion need to be adjusted.
And this works for other repeatable things, too, even if they don’t physically move. Sine and cosine just describe a position/distance/extent in perpendicular dimensions like north/east or x/y or voltage/time.
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