At the end of my second post on the position of the sun, I suggested as a challenge question determining the direction of sunrise or sunset on a solstice at the equator. I’m giving an illustration here showing the answer.
As is the case for many mathematical questions, visualization is key. We are very used to depictions of the sun and Earth where the latter is tilted on its axis. It is easier to consider the problem if we un-tilt our bearing and picture Earth’s axis as straight up-and-down with Earth rotating left-to-right (for points on the “front” side). Un-tilting Earth essentially means rotating our view.
Note that the image shown above is nothing more than the picture given in my first post on the position of the sun, but rotated 23.4 degrees. For the person at the blue dot, The sun is setting, she is about to be rotated into the dark area. Points to the north still have some daylight left, and the farther north you go, the longer the day is.
I think it is pretty clear from the picture that the sun is situated 23.4 degrees north of due west. For sunrise, the same type of picture could be drawn, but we would want Earth on the left-hand side of the drawing. Note that the same drawing would not work on other days. On the solstice, Earth’s tilt points directly at the sun, so this simple rotation is easy to visualize.