what does sin button do? I have always wondered why calculators have this function

Question

What is the sin button on a calculator used for? I have always wondered why and how you would use this function.

Answer 1

Here is a small primer without much detail: For a triangle $\triangle ABC$, you may calculate the quantities $\frac{AB}{BC},\frac{AB}{AC}$ and $\frac{BC}{AC}$. If you have another triangle that is similar to $\triangle ABC$, then the corresponding fractions for that triangle will evaluate to the same values (that's the idea of similar triangles).

Now, two triangles with all angles pairwise equal are similar. Say $\angle B$ of the triangle above is $90^\circ$, and we know the size of $\angle C$ (and therefore also $\angle A$). Then in theory, we should be able to tell what the three fractions above are without actually knowing the concrete size of the triangle, and we can. They are, in order, called $\tan C$, $\sin C$ and $\cos C$.

Answer 2

Sines, cosines and tangents are important for engineers who work on vibrations, sound waves, radio waves, and A/C electricity.
Any regular variation - temperature over a year, for example - can be modeled by sine waves.
They also turn out to be the answer to calculus questions, so mathematicians have to know about them.