Time, and Trig, and Conics, Oh MY!

A while back I wrote about the equation of time, recalling in part,

It came from a lesson in trig on simple harmonic motion. We were talking about things that demonstrated sinusoidal behavior, and one bright young man suggested that the height of the sun at noon would be an example. I sort of agreed with a comment about "not exactly at noon.. but" and then the little guy was confused.. "You know, I said, like today ."(it was Feb 12) "I think the sun was about 12 minutes late or so."
Slow looks at each other, then back to me... the three letter word look,,,,,"Huh?"
"You know, that's what the analemma is for, telling if the sun is early or late.".....

Same look, compounded by the wild eye..."HUH?"

See the whole blog here

So anyway, today I opened the blog over at "Square Circle Z" by Zac,(who seems to prefer to be called, "the mysterious Zac") and it showed a really nice use of the addition of two trig functions to explain the two components of the Equation of time. A nice exercise for people who tend to patienly explain to students who ask "What's that good for?"...(my personal first instinct is to throw things, but many administrations frown on that)