POSSIBLE SOLUTION(S)

This figure will be helpful and we shall refer to it in our solution.

These cells contain the code to generate this schematic offered above.

These cells contain the code to generate one of the schematics offered in the statement of the problem.

These cells contain the code to generate one of the graphic images offered in the statement of the problem.

We offer a slick, quick, elegant geometric solution as to why f(x) = cos(x). Our colleague Kurt Bryan, Department of Mathematics, Rose-Hulman Institute of Technology, saw this solution in a flash!

We present a more tedious analytic solution.