Under the sun

Well, I am not quite there yet... When will the sun be directly overhead? the answer is May 20, for PV.
Its a sine curve, with the equation
Lattitude = 23.5 x Sine (theta)

But theta is an angle, and you have to make it a percentage of the 92 day season between March 21 and June 21.

So here is a picture of the idea. Now, Hilo is 19.75 degrees north, so the date of overheadness is May 17, and if I leave on July 9, I will be crossing the sun's path again at 22 degrees north.