What Sin, Cos, and Tan are, your choice.
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*You might find [this page really helpful](https://www.mathsisfun.com/sine-cosine-tangent.html) to have open when reading about trig functions. It has some neat diagrams and handy interactive thingamies.*
Sine is a function. It is a maths thing where you give it an input number and it gives you some output number.
The word sine comes from the Latin sinus, the word for a pocket or lap, from the Arabic “jayb” meaning an opening or fold in a garment (and hence bosom or heart), as a misreading of the Arabic word for a chord (or the sine function itself), from the Sanskrit “jyā” for a bowstring. The basic trig functions have been in use for over a thousand years.
The bowstring thing comes from the fact that a bow, very roughly, forms the shape of two right-angled triangles, and the “sine” function very roughly tells you how long the bow is compared to the bowstring, when you’ve pulled it a certain amount.
At the basic level sine is all about triangles (although later on it turns out to be about circles).
The interesting thing about triangles is that if you scale them up (keeping the angles the same), the lengths of the sides stay in the same ratio; if one is double the length of another, no matter how big you make the triangle, that one will always be double the other. If you change angles, that ratio will change.
So the **sine** function gives us one of these ratios, specifically for a right-angled triangle (where one angle is 90 degrees, or a quarter circle). It tells us proportionally how much smaller the side furthers from the angle we’re looking at is than the the longest side (the one opposite the right angle). This is useful as if we know it for one triangle we know it for all similar triangles.
The “co” in **cosine** stands for “complement” (well, technically complementi, being Latin). Complementary angles are angles that add up to 90 degrees. So in a right-angled triangle, one angle must be 90 degrees, and the other two will be complementary angles (as the total angles inside a triangle must be 180 degrees). So the cosine of an angle is the sine of its complementary angle. It tells you the sine of the other angle in the triangle, or the ratio of the side next to your angle with the longest angle.
The problem with the right-angled triangle definition of these things is that it only works for angles between 0 and 90 degrees. But it turns out an easy way of extending sine and cosine beyond 90 degrees (and below 0 degrees) is to [use a circle](https://www.mathsisfun.com/algebra/trig-interactive-unit-circle.html) (remember that the size of the circle doesn’t matter, as we only care about the ratio of lengths – if we double the circle we double all sides, so the ratio stays the same). In that circle, as we go around it, for a particular angle from the centre, “sine” tells us how far up we are, “cosine” tells us how far along we are, and “tangent” tells us the length of the tangent to the circle at that point (more usefully it tells us the gradient of the line from the centre to that point, but that’s another matter).
One of the interesting things about the sine and cosine functions is that the rate at which each one changes (so how much sine goes up if you change the angle a bit) is proportional to the other one. This leads to them being very useful as solutions to certain maths and physics equations, particularly anything that is cyclical, i.e. repeats in a pattern (such as waves or signals). Sine and cosine then appear all over physics when dealing with waves or repeating patterns, and as quantum mechanics is all about things having wavefunctions, trig becomes very important when dealing with quantum mechanics (although usually we’ll be sneaky and use complex exponentials instead, but that’s another story).
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