TITLE: Why does $\sin(\cos x)=\cos(\sin y)$ result in a lattice of circles?
QUESTION [8 upvotes]: Using Desmos graphing, I made an equation $\sin(\cos x)=\cos(\sin y)$ (here) which resulted in a strange lattice of symbols. I know that the trigonometric functions relate a triangle's sides to its angles (SOHCAHTOA), so how does this equation create circles?

REPLY [5 votes]: I do like Desmos.  I want to like it more, but it does have limitations.  In this particular case, you can see how the loops arise quite clearly by plotting the 3D graphs of $z=\sin(\cos(x))$ and $z=\cos(\sin(y)$ on the same set of axes.  The result looks like so: