They are essentially a table of ratios for right triangles.
Referencing a corner/angle,
Sin is the ratio between the opposite side and the hypotenuse.
Cos is the ratio between the adjacent side and the hypotenuse.
Tan is the ratio between the opposite side and the adjacent side.
Your calculator just has a huge table of these ratios. Sin(30) has a specific number, because the opposite side divided by the hypotenuse will always be the same no matter how large or small that right triangle with a 30 degree corner is.
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