The seedling of this whole chalky project was born when I walked past a parking ramp at Colorado and 9th in Austin, Texas. The multiple-storied wall of this ramp is covered in 4 or 5-foot square squares of cement. It looks like enormous graph paper. I have this dream of putting some sine and cosine graphs on that ramp.
On this fine day in late June, though, Laurie and I were sitting outside a bakery in downtown Champaign and the sidewalk was this lovely grid. I refused to walk away without leaving a little periodic function.
As you may know Sine and Cosine are intimately related. The “co” in “cosine” references “complementary.” Complementary angles add up to 90 degrees – put them together and you have a right angle. If you get yourself a right triangle on a flat* surface, then the two acute angles are complementary. The sine of one of those cuties is the cosine of the other, and vice-versa.
The point is: Champaign’s new, nice little sinusoid (wavy) graph could be sine or cosine. Speaking of points, bonus points if you fill in the blank sin(x) = cos( _______ ).
* “flat” is used here to mean Euclidean. By now, you should know I am having fun, attempting to be precise, and making sure I am communicating.