What specifically do the cos, tan, and sin buttons do?

Meaning of "sin", "cos", "tan"
The ratio of two sides of any right triangle with the same interior angles is always the same number independent of the size of the triangle, the triangle's orientation, or the units used to measure the sides of the triangles. See similar right triangles for some specific example.

There are three ways to form a ratio of the three sides of a triangle (six if you count the inverse ratios also). The symbols "sin", "cos", and "tan" are the tags/labels we use to identify which ratio is which.

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Source: http://faculty.wwu.edu/vawter/PhysicsNet/Topics/Vectors/MeaningOfSine.html

When pressed each sends a tiny pulse of electricity to the keyboard interface.

An excellent answer hamilton.  Thank you.